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Ch. 6 Confidence Intervals

6.1 Confidence Intervals for the Mean (Large Samples)

1 Find a Critical Value

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.

1) Find the critical value zc that corresponds to a 95% confidence level.

A) ±1.96 B) ±2.575 C) ±2.33 D) ±1.645

2 Find the Margin of Error

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.

2) Determine the sampling error if the grade point averages for 10 randomly selected students from a class of 125

students has a mean of x = 1.8. Assume the grade point average of the 125 students has a mean of

μ = 2.4.

A) 0.6 B) 2.1 C) -0.6 D) 1.5

3) A random sample of 120 students has a test score average with a standard deviation of 9.2. Find the margin of

error if c = 0.98.

A) 1.96 B) 0.18 C) 0.84 D) 0.82

4) A random sample of 150 students has a grade point average with a standard deviation of 0.78. Find the margin

of error if c = 0.98.

A) 0.15 B) 0.08 C) 0.11 D) 0.12

5) A random sample of 40 students has a mean annual earnings of $3120 and a standard deviation of $677. Find

the margin of error if c = 0.95.

A) $210 B) $77 C) $2891 D) $7

3 Construct and Interpret Confidence Intervals for the Population Mean

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.

6) A random sample of 150 students has a grade point average with a mean of 2.86 and with a standard deviation

of 0.78. Construct the confidence interval for the population mean, μ, if c = 0.98.

A) (2.71, 3.01) B) (2.51, 3.53) C) (2.43, 3.79) D) (2.31, 3.88)

7) A random sample of 40 students has a test score with x = 81.5 and s = 10.2. Construct the confidence interval

for the population mean, μ if c = 0.90.

A) (78.8, 84.2) B) (51.8, 92.3) C) (66.3, 89.1) D) (71.8, 93.5)

8) A random sample of 40 students has a mean annual earnings of $3120 and a standard deviation of $677.

Construct the confidence interval for the population mean, μ if c = 0.95.

A) ($2910, $3330) B) ($210, $110) C) ($4812, $5342) D) ($1987, $2346)

9) A random sample of 56 fluorescent light bulbs has a mean life of 645 hours with a standard deviation of 31

hours. Construct a 95% confidence interval for the population mean.

A) (636.9, 653.1) B) (539.6, 551.2) C) (112.0, 118.9) D) (712.0, 768.0)

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10) A group of 49 randomly selected students has a mean age of 22.4 years with a standard deviation of 3.8.

Construct a 98% confidence interval for the population mean.

A) (21.1, 23.7) B) (20.3, 24.5) C) (19.8, 25.1) D) (18.8, 26.3)

11) A group of 40 bowlers showed that their average score was 192 with a standard deviation of 8. Find the 95%

confidence interval of the mean score of all bowlers.

A) (189.5, 194.5) B) (186.5, 197.5) C) (188.5, 195.6) D) (187.3, 196.1)

12) In a random sample of 60 computers, the mean repair cost was $150 with a standard deviation of $36.

Construct a 90% confidence interval for the population mean.

A) ($142, $158) B) ($138, $162) C) ($141, $159) D) ($537, $654)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

13) In a random sample of 60 computers, the mean repair cost was $150 with a standard deviation of $36.

a) Construct the 99% confidence interval for the population mean repair cost.

b) If the level of confidence was lowered to 95%, what will be the effect on the confidence interval?

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

14) In a recent study of 42 eighth graders, the mean number of hours per week that they watched television was

19.6 with a standard deviation of 5.8 hours. Find the 98% confidence interval for the population mean.

A) (17.5, 21.7) B) (14.1, 23.2) C) (18.3, 20.9) D) (19.1, 20.4)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

15) In a recent study of 54 eighth graders, the mean number of hours per week that they watched television was

19.5 with a standard deviation of 5.1 hours.

a) Find the 98% confidence interval of the mean.

b) If the standard deviation is doubled to 10.2, what will be the effect on the confidence interval?

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

16) In a sample of 10 randomly selected women, it was found that their mean height was 63.4 inches. From

previous studies, it is assumed that the standard deviation σ is 2.4 and that the population of height

measurements is normally distributed. Construct the 95% confidence interval for the population mean.

A) (61.9, 64.9) B) (58.1, 67.3) C) (59.7, 66.5) D) (60.8, 65.4)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

17) In a sample of 10 randomly selected women, it was found that their mean height was 63.4 inches. From

previous studies, it is assumed that the standard deviation, σ, is 2.4 inches and that the population of height

measurements is normally distributed.

a) Construct the 99% confidence interval for the population mean height of women.

b) If the sample size was doubled to 20 women, what will be the effect on the confidence interval?

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18) The numbers of advertisements seen or heard in one week for 30 randomly selected people in the United States

are listed below. Construct a 95% confidence interval for the true mean number of advertisements.

598 494 441 595 728 690 684 486 735 808

481 298 135 846 764 317 649 732 582 677

734 588 590 540 673 727 545 486 702 703

19) The number of wins in a season for 32 randomly selected professional football teams are listed below.

Construct a 90% confidence interval for the true mean number of wins in a season.

9 9 9 8 10 9 7 2

11 10 6 4 11 9 8 8

12 10 7 5 12 6 4 3

12 9 9 7 10 7 7 5

4 Determine the Minimum Sample Size

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.

20) The standard IQ test has a mean of 101 and a standard deviation of 16. We want to be 98% certain that we are

within 4 IQ points of the true mean. Determine the required sample size.

A) 87 B) 10 C) 188 D) 1

21) A nurse at a local hospital is interested in estimating the birth weight of infants. How large a sample must she

select if she desires to be 99% confident that the true mean is within 2 ounces of the sample mean? The

standard deviation of the birth weights is known to be 7 ounces.

A) 82 B) 81 C) 10 D) 9

22) In order to set rates, an insurance company is trying to estimate the number of sick days that full time workers

at an auto repair shop take per year. A previous study indicated that the standard deviation was 2.8 days. How

large a sample must be selected if the company wants to be 95% confident that the true mean differs from the

sample mean by no more than 1 day?

A) 31 B) 141 C) 512 D) 1024

23) In order to efficiently bid on a contract, a contractor wants to be 95% confident that his error is less than two

hours in estimating the average time it takes to install tile flooring. Previous contracts indicate that the

standard deviation is 4.5 hours. How large a sample must be selected?

A) 20 B) 4 C) 5 D) 19

24) In order to fairly set flat rates for auto mechanics, a shop foreman needs to estimate the average time it takes to

replace a fuel pump in a car. How large a sample must he select if he wants to be 99% confident that the true

average time is within 15 minutes of the sample average? Assume the standard deviation of all times is 30

minutes.

A) 27 B) 26 C) 6 D) 5

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SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

25) In order to set rates, an insurance company is trying to estimate the number of sick days that full time workers

at an auto repair shop take per year. A previous study indicated that the standard deviation was 2.8 days. a)

How large a sample must be selected if the company wants to be 90% confident that the true mean differs from

the sample mean by no more than 1 day? b) Repeat part (a) using a 95% confidence interval. Which level of

confidence requires a larger sample size? Explain.

5 Determine the Finite Population Correction Factor

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

26) There were 800 math instructors at a mathematics convention. Forty instructors were randomly selected and

given an IQ test. The scores produced a mean of 130 with a standard deviation of 10. Find a 95% confidence

interval for the mean of the 800 instructors. Use the finite population correction factor.

6 Concepts

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

27) A random sample of 200 high school seniors is given the SAT-V test. The mean score for this sample is x = 493.

What can you say about the mean score μ of all high school seniors?

28) The grade point averages for 10 randomly selected students in a statistics class with 125 students are listed

below. What can you say about the mean score μ of all 125 students?

2.1 3.1 2.0 3.9 3.5 3.7 2.8 1.9 2.5 2.2

29) A certain confidence in interval is 9.75 < μ < 11.05. Find the sample mean x and the error of estimate E.

30) Given the same sample statistics, which level of confidence will produce the narrowest confidence interval:

75%, 85%, 90%, or 95%? Explain your reasoning.

31) The grade point averages for 10 randomly selected students in a statistics class with 125 students are listed

below.

2.0 3.2 1.8 2.9 0.9 4.0 3.3 2.9 3.6 0.8

What is the effect on the width of the confidence interval if the sample size is increased to 20? Explain your

reasoning.

6.2 Confidence Intervals for the Mean (Small Samples)

1 Find a Critical Value

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.

1) Find the critical value, tc for c = 0.99 and n = 10.

A) 3.250 B) 3.169 C) 2.262 D) 1.833

2) Find the critical value, tc, for c = 0.95 and n = 16.

A) 2.131 B) 2.120 C) 2.602 D) 2.947

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3) Find the critical value, tc, for c = 0.90 and n = 15.

A) 1.761 B) 1.753 C) 2.145 D) 2.624

2 Construct and Interpret Confidence Intervals for the Population Mean

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.

4) Find the value of E, the margin of error, for c = 0.90, n = 16 and s = 2.5.

A) 1.1 B) 0.27 C) 0.84 D) 0.21

5) Find the value of E, the margin of error, for c = 0.99, n = 10 and s = 3.2.

A) 3.29 B) 2.85 C) 1.04 D) 3.21

6) Find the value of E, the margin of error, for c = 0.95, n = 15 and s = 5.2.

A) 2.88 B) 2.96 C) 2.36 D) 0.74

7) In a random sample of 28 families, the average weekly food expense was $95.60 with a standard deviation of

$22.50. Determine whether a normal distribution or a t-distribution should be used or whether neither of these

can be used to construct a confidence interval. Assume the distribution of weekly food expenses is normally

shaped.

A) Use the t-distribution.

B) Use normal distribution.

C) Cannot use normal distribution or t-distribution.

8) For a sample of 20 IQ scores the mean score is 105.8. The standard deviation, σ, is 15. Determine whether a

normal distribution or a t-distribution should be used or whether neither of these can be used to construct a

confidence interval. Assume that IQ scores are normally distributed.

A) Use normal distribution.

B) Use the t-distribution.

C) Cannot use normal distribution or t-distribution.

9) A random sample of 40 college students has a mean earnings of $3120 with a standard deviation of $677 over

the summer months. Determine whether a normal distribution or a t-distribution should be used or whether

neither of these can be used to construct a confidence interval.

A) Use normal distribution.

B) Use the t-distribution.

C) Cannot use normal distribution or t-distribution.

10) A random sample of 15 statistics textbooks has a mean price of $105 with a standard deviation of $30.25.

Determine whether a normal distribution or a t-distribution should be used or whether neither of these can be

used to construct a confidence interval. Assume the distribution of statistics textbook prices is not normally

distributed.

A) Cannot use normal distribution or t-distribution.

B) Use normal distribution.

C) Use the t-distribution.

11) Construct a 95% confidence interval for the population mean, μ. Assume the population has a normal

distribution. A sample of 20 college students had mean annual earnings of $3120 with a standard deviation of

$677.

A) ($2803, $3437) B) ($1324, $1567) C) ($2135, $2567) D) ($2657, $2891)

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12) Construct a 90% confidence interval for the population mean, μ. Assume the population has a normal

distribution. A sample of 15 randomly selected students has a grade point average of 2.86 with a standard

deviation of 0.78.

A) (2.51, 3.21) B) (2.41, 3.42) C) (2.37, 3.56) D) (2.28, 3.66)

13) Construct a 95% confidence interval for the population mean, μ. Assume the population has a normal

distribution. A sample of 25 randomly selected students has a mean test score of 81.5 with a standard deviation

of 10.2.

A) (77.29, 85.71) B) (56.12, 78.34) C) (66.35, 69.89) D) (87.12, 98.32)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

14) Construct a 98% confidence interval for the population mean, μ. Assume the population has a normal

distribution. A random sample of 20 college students has mean annual earnings of $3180 with a standard

deviation of $673.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

15) Construct a 95% confidence interval for the population mean, μ. Assume the population has a normal

distribution. A random sample of 16 fluorescent light bulbs has a mean life of 645 hours with a standard

deviation of 31 hours.

A) (628.5, 661.5) B) (876.2, 981.5) C) (531.2, 612.9) D) (321.7, 365.8)

16) Construct a 99% confidence interval for the population mean, μ. Assume the population has a normal

distribution. A group of 19 randomly selected students has a mean age of 22.4 years with a standard deviation

of 3.8 years.

A) (19.9, 24.9) B) (16.3, 26.9) C) (17.2, 23.6) D) (18.7, 24.1)

17) Construct a 98% confidence interval for the population mean, μ. Assume the population has a normal

distribution. A study of 14 bowlers showed that their average score was 192 with a standard deviation of 8.

A) (186.3, 197.7) B) (222.3, 256.1) C) (328.3, 386.9) D) (115.4, 158.8)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

18) Construct a 95% confidence interval for the population mean, μ. Assume the population has a normal

distribution. In a random sample of 26 computers, the mean repair cost was $149 with a standard deviation of

$39.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

19) Construct a 90% confidence interval for the population mean, μ. Assume the population has a normal

distribution. In a recent study of 22 eighth graders, the mean number of hours per week that they watched

television was 19.6 with a standard deviation of 5.8 hours.

A) (17.47, 21.73) B) (18.63, 20.89) C) (5.87, 7.98) D) (19.62, 23.12)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

20) a) Construct a 95% confidence interval for the population mean, μ. Assume the population has a normal

distribution. In a random sample of 26 computers, the mean repair cost was $129 with a standard deviation of

$37.

b) Suppose you did some research on repair costs for computers and found that the standard deviation is

σ = 37. Use the normal distribution to construct a 95% confidence interval for the population mean, μ. Compare

the results.

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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

21) A random sample of 10 parking meters in a beach community showed the following incomes for a day.

Assume the incomes are normally distributed.

$3.60 $4.50 $2.80 $6.30 $2.60 $5.20 $6.75 $4.25 $8.00 $3.00

Find the 95% confidence interval for the true mean.

A) ($3.39, $6.01) B) ($2.11, $5.34) C) ($4.81, $6.31) D) ($1.35, $2.85)

22) The grade point averages for 10 randomly selected high school students are listed below. Assume the grade

point averages are normally distributed.

2.0 3.2 1.8 2.9 0.9 4.0 3.3 2.9 3.6 0.8

Find a 98% confidence interval for the true mean.

A) (1.55, 3.53) B) (0.67, 1.81) C) (2.12, 3.14) D) (3.11, 4.35)

23) A local bank needs information concerning the checking account balances of its customers. A random sample

of 15 accounts was checked. The mean balance was $686.75 with a standard deviation of $256.20. Find a 98%

confidence interval for the true mean. Assume that the account balances are normally distributed.

A) ($513.17, $860.33) B) ($238.23, $326.41) C) ($326.21, $437.90) D) ($487.31, $563.80)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

24) A manufacturer receives an order for fluorescent light bulbs. The order requires that the bulbs have a mean life

span of 500 hours. The manufacturer selects a random sample of 25 fluorescent light bulbs and finds that they

have a mean life span of 495 hours with a standard deviation of 15 hours. Test to see if the manufacturer is

making acceptable light bulbs. Use a 95% confidence level. Assume the data are normally distributed.

25) A coffee machine is supposed to dispense 12 ounces of coffee in each cup. An inspector selects a random

sample of 40 cups of coffee and finds they have an average amount of 12.2 ounces with a standard deviation of

0.3 ounce. Use a 99% confidence interval to test whether the machine is dispensing acceptable amounts of

coffee.

6.3 Confidence Intervals for Population Proportions

1 Find a Point Estimate

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.

1) When 435 college students were surveyed,120 said they own their car. Find a point estimate for p, the

population proportion of students who own their cars.

A) 0.276 B) 0.724 C) 0.381 D) 0.216

2) A survey of 100 fatal accidents showed that 12 were alcohol related. Find a point estimate for p, the population

proportion of accidents that were alcohol related.

A) 0.12 B) 0.88 C) 0.136 D) 0.107

3) A survey of 400 non-fatal accidents showed that 189 involved the use of a cell phone. Find a point estimate for

p, the population proportion of non-fatal accidents that involved the use of a cell phone.

A) 0.472 B) 0.527 C) 0.896 D) 0.321

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4) A survey of 250 homeless persons showed that 17 were veterans. Find a point estimate p, for the population

proportion of homeless persons who are veterans.

A) 0.068 B) 0.932 C) 0.073 D) 0.064

5) A survey of 2650 golfers showed that 379 of them are left-handed. Find a point estimate for p, the population

proportion of golfers that are left-handed.

A) 0.143 B) 0.857 C) 0.167 D) 0.125

2 Construct and Interpret Confidence Intervals for the Population Proportion

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.

6) In a survey of 2480 golfers, 15% said they were left-handed. The surveyʹs margin of error was 3%. Construct a

confidence interval for the proportion of left-handed golfers.

A) (0.12, 0.18) B) (0.18, 0.21) C) (0.12, 0.15) D) (0.11, 0.19)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

7) The Federal Bureau of Labor Statistics surveyed 50,000 people and found the unemployment rate to be 5.8%.

The margin of error was 0.2%. Construct a confidence interval for the unemployment rate.

8) When 495 college students were surveyed, 150 said they own their car. Construct a 95% confidence interval for

the proportion of college students who say they own their cars.

9) A survey of 300 fatal accidents showed that 123 were alcohol related. Construct a 98% confidence interval for

the proportion of fatal accidents that were alcohol related.

10) A survey of 400 non-fatal accidents showed that 197 involved the use of a cell phone. Construct a 99%

confidence interval for the proportion of fatal accidents that involved the use of a cell phone.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

11) A survey of 280 homeless persons showed that 63 were veterans. Construct a 90% confidence interval for the

proportion of homeless persons who are veterans.

A) (0.184, 0.266) B) (0.176, 0.274) C) (0.167, 0.283) D) (0.161, 0.289)

12) A survey of 2450 golfers showed that 281 of them are left-handed. Construct a 98% confidence interval for the

proportion of golfers that are left-handed.

A) (0.100, 0.130) B) (0.203, 0.293) C) (0.369, 0.451) D) (0.683, 0.712)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

13) In a survey of 10 golfers, 2 were found to be left-handed. Is it practical to construct the 90% confidence interval

for the population proportion, p? Explain.

14) The USA Today claims that 44% of adults who access the Internet read the international news online. You

want to check the accuracy of their claim by surveying a random sample of 120 adults who access the Internet

and asking them if they read the international news online. Fifty-two adults responded ʺyes.ʺ Use a 95%

confidence interval to test the newspaperʹs claim.

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3 Determine the Minimum Sample Size

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.

15) A researcher at a major hospital wishes to estimate the proportion of the adult population of the United States

that has high blood pressure. How large a sample is needed in order to be 95% confident that the sample

proportion will not differ from the true proportion by more than 4%?

A) 601 B) 13 C) 1201 D) 423

16) A pollster wishes to estimate the proportion of United States voters who favor capital punishment. How large a

sample is needed in order to be 95% confident that the sample proportion will not differ from the true

proportion by more than 5%?

A) 385 B) 271 C) 10 D) 769

17) A private opinion poll is conducted for a politician to determine what proportion of the population favors

decriminalizing marijuana possession. How large a sample is needed in order to be 95% confident that the

sample proportion will not differ from the true proportion by more than 2%?

A) 2401 B) 1692 C) 4802 D) 25

18) A manufacturer of golf equipment wishes to estimate the number of left-handed golfers. How large a sample is

needed in order to be 98% confident that the sample proportion will not differ from the true proportion by

more than 2%? A previous study indicates that the proportion of left-handed golfers is 8%.

A) 999 B) 707 C) 1086 D) 17

19) A researcher wishes to estimate the number of households with two cars. How large a sample is needed in

order to be 98% confident that the sample proportion will not differ from the true proportion by more than 5%?

A previous study indicates that the proportion of households with two cars is 19%.

A) 335 B) 237 C) 413 D) 8

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

20) A state highway patrol official wishes to estimate the number of drivers that exceed the speed limit traveling a

certain road.

a) How large a sample is needed in order to be 95% confident that the sample proportion will not differ from

the true proportion by more than 2%?

b) Repeat part (a) assuming previous studies found that 70% of drivers on this road exceeded the speed limit.

6.4 Confidence Intervals for Variance and Standard Deviation

1 Find Critical Values

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.

1) Find the critical values, X 2

R andX 2

L , for c = 0.95 and n = 12.

A) 3.816 and 21.920 B) 3.053 and 24.725 C) 4.575 and 26.757 D) 2.603 and 19.675

2) Find the critical values, X 2

R andX 2

L , for c = 0.90 and n = 15.

A) 6.571 and 23.685 B) 4.075 and 31.319 C) 4.660 and 29.131 D) 5.629 and 26.119

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3) Find the critical values, X 2

R andX 2

L , for c = 0.98 and n = 20.

A) 7.633 and 36.191 B) 6.844 and 27.204 C) 8.907 and 38.582 D) 10.117 and 32.852

4) Find the critical values, X 2

R andX 2

L , for c = 0.99 and n = 10.

A) 1.735 and 23.587 B) 2.156 and 25.188 C) 2.088 and 21.666 D) 2.558 and 23.209

2 Construct Confidence Intervals for the Population Variance and Population Standard Deviation

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Assume the sample is taken from a normally distributed population and construct the indicated confidence interval.

5) Construct a 95% confidence interval for the population standard deviation σ of a random sample of 15 men

who have a mean weight of 165.2 pounds with a standard deviation of 13.5 pounds. Assume the population is

normally distributed.

A) (9.9, 21.3) B) (97.7, 453.3) C) (2.7, 5.8) D) (10.4, 19.7)

6) A random sample of 16 men have a mean height of 67.5 inches and a standard deviation of 1.5 inches.

Construct a 99% confidence interval for the population standard deviation, σ.

A) (1.0, 2.7) B) (1.0, 2.8) C) (0.8, 2.2) D) (1.1, 2.5)

7) A random sample of 20 women have a mean height of 62.5 inches and a standard deviation of 3.2 inches.

Construct a 98% confidence interval for the population variance, σ2.

A) (5.4, 25.5) B) (2.3, 5.0) C) (1.7, 8.0) D) (5.7, 26.8)

8) The heights (in inches) of 20 randomly selected adult males are listed below. Construct a 99% confidence

interval for the variance, σ2.

70 72 71 70 69 73 69 68 70 71

67 71 70 74 69 68 71 71 71 72

A) (1.47, 8.27) B) (21.61, 69.06) C) (1.35, 8.43) D) (2.16, 71.06)

9) The grade point averages for 10 randomly selected students are listed below. Construct a 90% confidence

interval for the population standard deviation, σ.

2.0 3.2 1.8 2.9 0.9 4.0 3.3 2.9 3.6 0.8

A) (0.81, 1.83) B) (0.32, 0.85) C) (0.53, 1.01) D) (1.10, 2.01)

10) The mean replacement time for a random sample of 12 microwave ovens is 8.6 years with a standard deviation

of 4.2 years. Construct the 98% confidence interval for the population variance, σ2.

A) (7.8, 63.6) B) (2.8, 8.0) C) (1.9, 15.1) D) (7.4, 54.3)

11) A student randomly selects 10 CDs at a store. The mean is $13.75 with a standard deviation of $1.50. Construct

a 95% confidence interval for the population standard deviation, σ.

A) ($1.03, $2.74) B) ($0.99, $2.50) C) ($1.06, $7.51) D) ($0.84, $2.24)

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12) The stem-and-leaf plot shows the test scores of 16 randomly selected students. Construct a 99% confidence

interval for the population standard deviation.

56789

9

5 8 3

7 4 4 2 9

5 8 3 5

3 1 7

A) (7.61, 20.33) B) (57.97, 413.27) C) (62.18, 363.63) D) (7.89, 19.07)

13) The dotplot shows the weights (in pounds) of 15 dogs selected randomly from those adopted out by an animal

shelter last week. Construct a 98% confidence interval for the population variance.

Weights

25 30 35

Pounds

A) (3.03, 18.97) B) (1.74, 4.36) C) (3.38, 15.70) D) (2.89, 16.91)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

14) A container of car oil is supposed to contain 1000 milliliters of oil. A quality control manager wants to be sure

that the standard deviation of the oil containers is less than 20 milliliters. He randomly selects 10 cans of oil

with a mean of 997 milliliters and a standard deviation of 32 milliliters. Use these sample results to construct a

95% confidence interval for the true value of σ. Does this confidence interval suggest that the variation in the oil

containers is at an acceptable level?

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Ch. 6 Confidence Intervals

Answer Key

6.1 Confidence Intervals for the Mean (Large Samples)

1 Find a Critical Value

1) A

2 Find the Margin of Error

2) A

3) A

4) A

5) A

3 Construct and Interpret Confidence Intervals for the Population Mean

6) A

7) A

8) A

9) A

10) A

11) A

12) A

13) a) ($138, $162)

b) A decrease in the level of confidence will decrease the width of the confidence interval.

14) A

15) a) (17.9, 21.1)

b) An increase in the standard deviation will widen the confidence interval.

16) A

17) a) (61.4, 65.4)

b) An increase in the sample size will decrease the width of the confidence interval.

18) (543.8, 658. 0)

19) (7.2, 8.8)

4 Determine the Minimum Sample Size

20) A

21) A

22) A

23) A

24) A

25) a) 22

b) 31; A 95% confidence interval requires a larger sample than a 90% confidence interval because more information is

needed from the population to be 95% confident.

5 Determine the Finite Population Correction Factor

26) (127.0, 133.0)

6 Concepts

27) The sample mean x = 493 is the best estimator of the unknown population mean μ.

28) The sample mean x = 2.77 is the best point estimate of the unknown population mean μ.

29) Sample mean x = 10.40 and the error of estimate E = 0.65.

30) The 75% level of confidence will produce the narrowest confidence interval. As the level of confidence decreases, zc

decreases, causing narrower intervals.

31) The width of the interval will decrease. As n increases, E decreases because n is in the denominator of the formula

for E. So the intervals become narrower.

6.2 Confidence Intervals for the Mean (Small Samples)

1 Find a Critical Value

1) A

2) A

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3) A

2 Construct and Interpret Confidence Intervals for the Population Mean

4) A

5) A

6) A

7) A

8) A

9) A

10) A

11) A

12) A

13) A

14) ($2798, $3562)

15) A

16) A

17) A

18) ($133.24, $164.76)

19) A

20) a) ($114.05, $143.95)

b) ($114.78, $143.22); The t-confidence interval is wider.

21) A

22) A

23) A

24) (488.81, 501.19). Because the interval contains the desired life span of 500 hours, they are making good light bulbs.

25) (12.1, 12.3) Because the interval does not contain the desired amount of 12 ounces, the machine is not working

properly.

6.3 Confidence Intervals for Population Proportions

1 Find a Point Estimate

1) A

2) A

3) A

4) A

5) A

2 Construct and Interpret Confidence Intervals for the Population Proportion

6) A

7) (0.058, 0.060)

8) (0.263, 0.344)

9) (0.344, 0.476)

10) (0.428, 0.557)

11) A

12) A

13) It is not practical to find the confidence interval. It is necessary that np^ > 5 to insure that the

distribution of p ^ be normal. (np ^

= 2)

14) (0.345, 0.522) Because the interval contains the reported percentage of 44%, the newspaperʹs claim is accurate.

3 Determine the Minimum Sample Size

15) A

16) A

17) A

18) A

19) A

20) a) 2401

b) 2017

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6.4 Confidence Intervals for Variance and Standard Deviation

1 Find Critical Values

1) A

2) A

3) A

4) A

2 Construct Confidence Intervals for the Population Variance and Population Standard Deviation

5) A

6) A

7) A

8) A

9) A

10) A

11) A

12) A

13) A

14) The 95% confidence interval is (22.01, 58.42). Because this interval does not contain 20, the data suggest that the

standard deviation is not at an acceptable level.

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Ch. 7 Hypothesis Testing with One Sample

7.1 Introduction to Hypothesis Testing

1 State a Null and Alternative Hypothesis

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

1) The mean age of bus drivers in Chicago is 48.5 years. Write the null and alternative hypotheses.

2) The mean IQ of statistics teachers is greater than 110. Write the null and alternative hypotheses.

3) The mean score for all NBA games during a particular season was less than 101 points per game. Write the null

and alternative hypotheses.

4) A candidate for governor of a particular state claims to be favored by at least half of the voters. Write the null

and alternative hypotheses.

5) The dean of a major university claims that the mean time for students to earn a Masterʹs degree is at most 4.9

years. Write the null and alternative hypotheses.

6) The buyer of a local hiking club store recommends against buying the new digital altimeters because they vary

more than the old altimeters, which had a standard deviation of one yard. Write the null and alternative

hypotheses.

7) The mean age of bus drivers in Chicago is 53.7 years. State this claim mathematically. Write the null and

alternative hypotheses. Identify which hypothesis is the claim.

8) The mean IQ of statistics teachers is greater than 120. State this claim mathematically. Write the null and

alternative hypotheses. Identify which hypothesis is the claim.

9) The mean score for all NBA games during a particular season was less than 101 points per game. State this

claim mathematically. Write the null and alternative hypotheses. Identify which hypothesis is the claim.

10) A candidate for governor of a particular state claims to be favored by at least half of the voters. State this claim

mathematically. Write the null and alternative hypotheses. Identify which hypothesis is the claim.

11) The dean of a major university claims that the mean time for students to earn a Masterʹs degree is at most 3.3

years. State this claim mathematically. Write the null and alternative hypotheses. Identify which hypothesis is

the claim.

12) The buyer of a local hiking club store recommends against buying the new digital altimeters because they vary

more than the old altimeters, which had a standard deviation of one yard. State this claim mathematically.

Write the null and alternative hypotheses. Identify which hypothesis is the claim.

2 Identify Whether to Use a One-tailed or Two-tailed Test

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.

13) Given H0: p ≥ 80% and Ha: p < 80%, determine whether the hypothesis test is left-tailed, right-tailed, or

two-tailed.

A) left-tailed B) right-tailed C) two-tailed

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14) Given H0: μ ≤ 25 and Ha: μ > 25, determine whether the hypothesis test is left-tailed, right-tailed, or

two-tailed.

A) right-tailed B) left-tailed C) two-tailed

15) A researcher claims that 62% of voters favor gun control. Determine whether the hypothesis test for this claim

is left-tailed, right-tailed, or two-tailed.

A) two-tailed B) left-tailed C) right-tailed

16) A brewery claims that the mean amount of beer in their bottles is at least 12 ounces. Determine whether the

hypothesis test for this claim is left-tailed, right-tailed, or two-tailed.

A) left-tailed B) right-tailed C) two-tailed

17) A car maker claims that its new sub-compact car gets better than 47 miles per gallon on the highway.

Determine whether the hypothesis test for this is left-tailed, right-tailed, or two-tailed.

A) right-tailed B) left-tailed C) two-tailed

18) The owner of a professional basketball team claims that the mean attendance at games is over 30,000 and

therefore the team needs a new arena. Determine whether the hypothesis test for this claim is left-tailed,

right-tailed, or two-tailed.

A) right-tailed B) left-tailed C) two-tailed

19) An elementary school claims that the standard deviation in reading scores of its fourth grade students is less

than 4.35. Determine whether the hypothesis test for this claim is left-tailed, right-tailed, or two-tailed.

A) left-tailed B) right-tailed C) two-tailed

3 Identify Type I and Type II Errors

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

20) The mean age of bus drivers in Chicago is 52.5 years. Identify the type I and type II errors for the hypothesis

test of this claim.

21) The mean IQ of statistics teachers is greater than 120. Identify the type I and type II errors for the hypothesis

test of this claim.

22) The mean score for all NBA games during a particular season was less than 105 points per game. Identify the

type I and type II errors for the hypothesis test of this claim.

23) A candidate for governor of a certain state claims to be favored by at least half of the voters. Identify the type I

and type II errors for the hypothesis test of this claim.

4 Interpret a Decision Based on the Results of a Statistical Test

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.

24) The mean age of bus drivers in Chicago is 50.2 years. If a hypothesis test is performed, how should you

interpret a decision that rejects the null hypothesis?

A) There is sufficient evidence to reject the claim μ = 50.2.

B) There is not sufficient evidence to reject the claim μ = 50.2.

C) There is sufficient evidence to support the claim μ = 50.2.

D) There is not sufficient evidence to support the claim μ = 50.2.

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25) The mean age of bus drivers in Chicago is 59.3 years. If a hypothesis test is performed, how should you

interpret a decision that fails to reject the null hypothesis?

A) There is not sufficient evidence to reject the claim μ = 59.3.

B) There is sufficient evidence to reject the claim μ = 59.3.

C) There is sufficient evidence to support the claim μ = 59.3.

D) There is not sufficient evidence to support the claim μ = 59.3.

26) The mean age of bus drivers in Chicago is greater than 57.8 years. If a hypothesis test is performed, how should

you interpret a decision that rejects the null hypothesis?

A) There is sufficient evidence to support the claim μ > 57.8.

B) There is sufficient evidence to reject the claim μ > 57.8.

C) There is not sufficient evidence to reject the claim μ > 57.8.

D) There is not sufficient evidence to support the claim μ > 57.8.

27) The mean age of bus drivers in Chicago is greater than 47.6 years. If a hypothesis test is performed, how should

you interpret a decision that fails to reject the null hypothesis?

A) There is not sufficient evidence to support the claim μ > 47.6.

B) There is sufficient evidence to reject the claim μ > 47.6.

C) There is not sufficient evidence to reject the claim μ > 47.6.

D) There is sufficient evidence to support the claim μ > 47.6.

28) The mean IQ of statistics teachers is greater than 160. If a hypothesis test is performed, how should you

interpret a decision that rejects the null hypothesis?

A) There is sufficient evidence to support the claim μ > 160.

B) There is sufficient evidence to reject the claim μ > 160.

C) There is not sufficient evidence to reject the claim μ > 160.

D) There is not sufficient evidence to support the claim μ > 160.

29) The mean IQ of statistics teachers is greater than 150. If a hypothesis test is performed, how should you

interpret a decision that fails to reject the null hypothesis?

A) There is not sufficient evidence to support the claim μ > 150.

B) There is sufficient evidence to reject the claim μ > 150.

C) There is not sufficient evidence to reject the claim μ > 150.

D) There is sufficient evidence to support the claim μ > 150.

30) The mean score for all NBA games during a particular season was less than 92 points per game. If a hypothesis

test is performed, how should you interpret a decision that rejects the null hypothesis?

A) There is sufficient evidence to support the claim μ < 92.

B) There is sufficient evidence to reject the claim μ < 92.

C) There is not sufficient evidence to reject the claim μ < 92.

D) There is not sufficient evidence to support the claim μ < 92.

31) The mean score for all NBA games during a particular season was less than 100 points per game. If a

hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis?

A) There is not sufficient evidence to support the claim μ < 100.

B) There is sufficient evidence to reject the claim μ < 100.

C) There is not sufficient evidence to reject the claim μ < 100.

D) There is sufficient evidence to support the claim μ < 100.

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32) A candidate for governor of a certain state claims to be favored by at least half of the voters. If a hypothesis test

is performed, how should you interpret a decision that rejects the null hypothesis?

A) There is sufficient evidence to reject the claim ρ ≥ 0.5.

B) There is not sufficient evidence to reject the claim ρ ≥ 0.5.

C) There is sufficient evidence to support the claim ρ ≥ 0.5.

D) There is not sufficient evidence to support the claim ρ ≥ 0.5.

33) A candidate for governor of a certain state claims to be favored by at least half of the voters. If a hypothesis test

is performed, how should you interpret a decision that fails to reject the null hypothesis?

A) There is not sufficient evidence to reject the claim ρ ≥ 0.5.

B) There is sufficient evidence to reject the claim ρ ≥ 0.5.

C) There is sufficient evidence to support the claim ρ ≥ 0.5.

D) There is not sufficient evidence to support the claim ρ ≥ 0.5.

34) The dean of a major university claims that the mean time for students to earn a Masterʹs degree is at most 5.8

years. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?

A) There is sufficient evidence to reject the claim μ ≤ 5.8.

B) There is not sufficient evidence to reject the claim μ ≤ 5.8.

C) There is sufficient evidence to support the claim μ ≤ 5.8.

D) There is not sufficient evidence to support the claim μ ≤ 5.8.

35) The dean of a major university claims that the mean time for students to earn a Masterʹs degree is at most 5.1

years. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null

hypothesis?

A) There is not sufficient evidence to reject the claim μ ≤ 5.1.

B) There is sufficient evidence to reject the claim μ ≤ 5.1.

C) There is sufficient evidence to support the claim μ ≤ 5.1.

D) There is not sufficient evidence to support the claim μ ≤ 5.1.

5 Use Confidence Intervals to Make Decisions

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.

36) Given H0: μ ≤ 12, for which confidence interval should you reject H0?

A) (13, 16) B) (11.5, 12.5) C) (10, 13)

37) Given H0: p ≥ 0.45, for which confidence interval should you reject H0?

A) (0.32, 0.40) B) (0.40, 0.50) C) (0.42, 0.47)

6 Concepts

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.

38) Given H0: p = 0.85 and α = 0.10, which level of confidence should you use to test the claim?

A) 90% B) 95% C) 99% D) 80%

39) Given H0: μ ≥ 23.5 and α = 0.05, which level of confidence should you use to test the claim?

A) 90% B) 99% C) 80% D) 95%

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7.2 Hypothesis Testing for the Mean (Large Samples)

1 Find P-values

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.

1) Suppose you are using α = 0.05 to test the claim that μ > 14 using a P-value. You are given the sample statistics

n = 50, x = 14.3, and s = 1.2. Find the P-value.

A) 0.0384 B) 0.1321 C) 0.0128 D) 0.0012

2) Suppose you are using α = 0.05 to test the claim that μ ≠ 14 using a P-value. You are given the sample statistics

n = 35, x = 13.1, and s = 2.7. Find the P-value.

A) 0.0488 B) 0.0591 C) 0.1003 D) 0.0244

3) Suppose you are using α = 0.01 to test the claim that μ ≤ 32 using a P-value. You are given the sample statistics

n = 40, x = 33.8, and s = 4.3. Find the P-value.

A) 0.0040 B) 0.9960 C) 0.0211 D) 0.1030

4) Suppose you are using α = 0.01 to test the claim that μ = 1620 using a P-value. You are given the sample

statistics n = 35, x = 1590, and s = 82. Find the P-value.

A) 0.0308 B) 0.0154 C) 0.3169 D) 0.0077

2 Test a Claim About a Mean Using P-values

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.

5) Given H0: μ = 25, Ha: μ ≠ 25, and P = 0.034. Do you reject or fail to reject H0 at the 0.01 level of significance?

A) fail to reject H0

B) reject H0

C) not sufficient information to decide

6) Given H0: μ ≥ 18 and P = 0.070. Do you reject or fail to reject H0 at the 0.05 level of significance?

A) fail to reject H0

B) reject H0

C) not sufficient information to decide

7) Given Ha: μ > 85 and P = 0.007. Do you reject or fail to reject H0 at the 0.01 level of significance?

A) reject H0

B) fail to reject H0

C) not sufficient information to decide

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

8) A fast food outlet claims that the mean waiting time in line is less than 3.4 minutes. A random sample of 60

customers has a mean of 3.3 minutes with a standard deviation of 0.6 minute. If α = 0.05, test the fast food

outletʹs claim.

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9) A local school district claims that the number of school days missed by its teachers due to illness is below the

national average of 5. A random sample of 40 teachers provided the data below. At α = 0.05, test the districtʹs

claim using P-values.

0 3 6 3 3 5 4 1 3 5

7 3 1 2 3 3 2 4 1 6

2 5 2 8 3 1 2 5 4 1

1 1 2 1 5 7 5 4 9 3

3 Find Critical Values

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.

10) Find the critical value for a right-tailed test with α = 0.01 and n = 75.

A) 2.33 B) 2.575 C) 1.645 D) 1.96

11) Find the critical value for a two-tailed test with α = 0.01 and n = 30.

A) ±2.575 B) ±2.33 C) ±1.645 D) ±1.96

12) Find the critical value for a left-tailed test with α = 0.05 and n = 48.

A) -1.645 B) -2.33 C) -2.575 D) -1.96

13) Find the critical value for a two-tailed test with α = 0.10 and n = 100.

A) ±1.645 B) ±2.33 C) ±2.575 D) ±1.96

14) Find the critical value for a left-tailed test with α = 0.025 and n = 50.

A) -1.96 B) -2.33 C) -2.575 D) -1.645

15) Find the critical value for a two-tailed test with α = 0.07 and n = 36.

A) ±1.81 B) ±2.33 C) ±2.575 D) ±1.96

4 Test a Claim About a Mean

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.

16) You wish to test the claim that μ > 32 at a level of significance of α = 0.05 and are given sample statistics n = 50,

x = 32.3, and s = 1.2. Compute the value of the standardized test statistic. Round your answer to two decimal

places.

A) 1.77 B) 2.31 C) 0.98 D) 3.11

17) You wish to test the claim that μ ≠ 22 at a level of significance of α = 0.05 and are given sample statistics n = 35,

x = 21.1, and s = 2.7. Compute the value of the standardized test statistic. Round your answer to two decimal

places.

A) -1.97 B) -3.12 C) -2.86 D) -1.83

18) You wish to test the claim that μ ≤ 38 at a level of significance of α = 0.01 and are given sample statistics n = 40,

x = 39.8, and s = 4.3. Compute the value of the standardized test statistic. Round your answer to two decimal

places.

A) 2.65 B) 3.51 C) 2.12 D) 1.96

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19) You wish to test the claim that μ = 1240 at a level of significance of α = 0.01 and are given sample statistics

n = 35, x = 1210 and s = 82. Compute the value of the standardized test statistic. Round your answer to two

decimal places.

A) -2.16 B) -3.82 C) -4.67 D) -5.18

20) Suppose you want to test the claim that μ ≠ 3.5. Given a sample size of n = 47 and a level of significance of

α = 0.10, when should you reject H0 ?

A) Reject H0 if the standardized test statistic is greater than 1.645 or less than -1.645.

B) Reject H0 if the standardized test statistic is greater than 2.575 or less than -2.575.

C) Reject H0 if the standardized test statistic is greater than 2.33 or less than -2.33

D) Reject H0 if the standardized test statistic is greater than 1.96 or less than -1.96

21) Suppose you want to test the claim that μ ≤ 25.6. Given a sample size of n = 53 and a level of significance of

α = 0.01, when should you reject H0?

A) Reject H0 if the standardized test statistic is greater than 2.33.

B) Reject H0 if the standardized test statistic is greater than 1.96.

C) Reject H0 if the standardized test statistic is greater than 1.645.

D) Reject H0 if the standardized test statistic is greater than 2.575.

22) Suppose you want to test the claim that μ ≥ 65.4. Given a sample size of n = 35 and a level of significance of

α = 0.05, when should you reject H0?

A) Reject H0 if the standardized test statistic is less than -1.645.

B) Reject H0 if the standardized test is less than -1.96.

C) Reject H0 if the standardized test statistic is less than -2.575.

D) Reject H0 if the standardized test statistic is less than -1.28.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

23) Test the claim that μ > 19, given that α = 0.05 and the sample statistics are n = 50, x = 19.3, and s = 1.2.

24) Test the claim that μ ≠ 38, given that α = 0.05 and the sample statistics are n = 35, x = 37.1 and s = 2.7.

25) Test the claim that μ ≤ 22, given that α = 0.01 and the sample statistics are n = 40, x = 23.8, and s = 4.3.

26) Test the claim that μ = 1210, given that α = 0.01 and the sample statistics are n = 35, x = 1180, and s = 82.

27) A local brewery distributes beer in bottles labeled 12 ounces. A government agency thinks that the brewery is

cheating its customers. The agency selects 50 of these bottles, measures their contents, and obtains a sample

mean of 11.7 ounces with a standard deviation of 0.70 ounce. Use a 0.01 significance level to test the agencyʹs

claim that the brewery is cheating its customers.

28) A manufacturer claims that the mean lifetime of its fluorescent bulbs is 1000 hours. A homeowner selects 40

bulbs and finds the mean lifetime to be 980 hours with a standard deviation of 80 hours. Test the

manufacturerʹs claim. Use α = 0.05.

29) A trucking firm suspects that the mean lifetime of a certain tire it uses is less than 34,000 miles. To check the

claim, the firm randomly selects and tests 54 of these tires and gets a mean lifetime of 33,390 miles with a

standard deviation of 1200 miles. At α = 0.05, test the trucking firmʹs claim.

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30) A local politician, running for reelection, claims that the mean prison time for car thieves is less than the

required 4 years. A sample of 80 convicted car thieves was randomly selected, and the mean length of prison

time was found to be 3 years and 6 months, with a standard deviation of 1 year and 3 months. At α = 0.05, test

the politicianʹs claim.

31) A local group claims that the police issue at least 60 speeding tickets a day in their area. To prove their point,

they randomly select one month. Their research yields the number of tickets issued for each day. The data are

listed below. At α = 0.01, test the groupʹs claim.

70 48 41 68 69 55 70 57 60 83

32 60 72 58 88 48 59 60 56 65

66 60 68 42 57 59 49 70 75 63

44

32) A fast food outlet claims that the mean waiting time in line is less than 3.5 minutes. A random sample of 60

customers has a mean of 3.6 minutes with a standard deviation of 0.6 minute. If α = 0.05, test the fast food

outletʹs claim using critical values and rejection regions.

33) A fast food outlet claims that the mean waiting time in line is less than 3.5 minutes. A random sample of 60

customers has a mean of 3.6 minutes with a standard deviation of 0.6 minute. If α = 0.05, test the fast food

outletʹs claim using confidence intervals.

34) A local school district claims that the number of school days missed by teachers due to illness is below the

national average of 5 days. A random sample of 40 teachers provided the data below. At α = 0.05, test the

districtʹs claim using critical values and rejection regions.

0 3 6 3 3 5 4 1 3 5

7 3 1 2 3 3 2 4 1 6

2 5 2 8 3 1 2 5 4 1

1 1 2 1 5 7 5 4 9 3

35) A local school district claims that the number of school days missed by teachers due to illness is below the

national average of 5. A random sample of 40 teachers provided the data below. At α = 0.05, test the districtʹs

claim using confidence intervals.

0 3 6 3 3 5 4 1 3 5

7 3 1 2 3 3 2 4 1 6

2 5 2 8 3 1 2 5 4 1

1 1 2 1 5 7 5 4 9 3

7.3 Hypothesis Testing for the Mean (Small Samples)

1 Find Critical Values in a t-distribution

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.

1) Find the critical values for a sample with n = 15 and α = 0.05 if H0: μ ≤ 20.

A) 1.761 B) 2.977 C) 2.625 D) 1.345

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2 Test a Claim About a Mean

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.

2) Find the standardized test statistic t for a sample with n = 12, x = 22.2, s = 2.2, and α = 0.01 if H0: μ = 21. Round

your answer to three decimal places.

A) 1.890 B) 1.991 C) 2.132 D) 2.001

3) Find the standardized test statistic t for a sample with n = 10, x = 9.7, s = 1.3, and α = 0.05 if H0: μ ≥ 10.6. Round

your answer to three decimal places.

A) -2.189 B) -3.186 C) -3.010 D) -2.617

4) Find the standardized test statistic t for a sample with n = 15, x = 7.4, s = 0.8, and α = 0.05 if H0: μ ≤ 7.1. Round

your answer to three decimal places.

A) 1.452 B) 1.728 C) 1.631 D) 1.312

5) Find the standardized test statistic t for a sample with n = 20, x = 13, s = 2.0, and α = 0.05 if Ha: μ < 13.4. Round

your answer to three decimal places.

A) -0.894 B) -0.872 C) -1.265 D) -1.233

6) Find the standardized test statistic t for a sample with n = 25, x = 36, s = 3, and α = 0.005 if Ha: μ > 35. Round

your answer to three decimal places.

A) 1.667 B) 1.997 C) 1.452 D) 1.239

7) Find the standardized test statistic t for a sample with n = 12, x = 18.8, s = 2.1, and α = 0.01 if Ha: μ ≠ 19.3.

Round your answer to three decimal places.

A) -0.825 B) -0.008 C) -0.037 D) -0.381

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

8) Use a t-test to test the claim μ = 16 at α = 0.01, given the sample statistics n = 12, x = 17.2, and s = 2.2.

9) Use a t-test to test the claim μ ≥ 10.2 at α = 0.05, given the sample statistics n = 10, x = 9.3, and s = 1.3.

10) Use a t-test to test the claim μ ≤ 8.8 at α = 0.05, given the sample statistics n = 15, x = 9.1, and s = 0.8.

11) Use a t-test to test the claim μ < 11 at α = 0.10, given the sample statistics n = 20, x = 10.6, and s = 2.0.

12) Use a t-test to test the claim μ > 39 at α = 0.005, given the sample statistics n = 25, x = 40, and s = 3.

13) Use a t-test to test the claim μ = 23.3 at α = 0.01, given the sample statistics n = 12, x = 22.8, and s = 2.1.

14) The Metropolitan Bus Company claims that the mean waiting time for a bus during rush hour is less than 10

minutes. A random sample of 20 waiting times has a mean of 8.6 minutes with a standard deviation of 2.1

minutes. At α = 0.01, test the bus companyʹs claim. Assume the distribution is normally distributed.

15) A local brewery distributes beer in bottles labeled 12 ounces. A government agency thinks that the brewery is

cheating its customers. The agency selects 20 of these bottles, measures their contents, and obtains a sample

mean of 11.7 ounces with a standard deviation of 0.7 ounce. Use a 0.01 significance level to test the agencyʹs

claim that the brewery is cheating its customers.

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16) A local group claims that the police issue more than 60 speeding tickets a day in their area. To prove their

point, they randomly select two weeks. Their research yields the number of tickets issued for each day. The

data are listed below. At α = 0.01, test the groupʹs claim.

70 48 41 68 69 55 70

57 60 83 32 60 72 58

17) A local group claims that the police issue more than 60 speeding tickets a day in their area. To prove their

point, they randomly select two weeks. Their research yields the number of tickets issued for each day. The

data are listed below. At α = 0.02, test the groupʹs claim using confidence intervals.

70 48 41 68 69 55 70

57 60 83 32 60 72 58

18) A manufacturer claims that the mean lifetime of its fluorescent bulbs is 1100 hours. A homeowner selects 25

bulbs and finds the mean lifetime to be 1070 hours with a standard deviation of 80 hours. Test the

manufacturerʹs claim. Use α = 0.05.

19) A manufacturer claims that the mean lifetime of its fluorescent bulbs is 1000 hours. A homeowner selects 25

bulbs and finds the mean lifetime to be 980 hours with a standard deviation of 80 hours. If α = 0.05, test the

manufacturerʹs claim using confidence intervals.

20) A trucking firm suspects that the mean life of a certain tire it uses is less than 35,000 miles. To check the claim,

the firm randomly selects and tests 18 of these tires and gets a mean lifetime of 34,400 miles with a standard

deviation of 1200 miles. At α = 0.05, test the trucking firmʹs claim.

3 Test a Claim About a Mean Using a P-value

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

21) A local group claims that the police issue more than 60 speeding tickets a day in their area. To prove their

point, they randomly select two weeks. Their research yields the number of tickets issued for each day. The

data are listed below. At α = 0.01, test the groupʹs claim using P-values.

70 48 41 68 69 55 70

57 60 83 32 60 72 58

22) A manufacturer claims that the mean lifetime of its fluorescent bulbs is 1000 hours. A homeowner selects 25

bulbs and finds the mean lifetime to be 980 hours with a standard deviation of 80 hours. If α = 0.05, test the

manufacturerʹs claim using P-values.

23) A fast food outlet claims that the mean waiting time in line is less than 3.3 minutes. A random sample of 20

customers has a mean of 3.1 minutes with a standard deviation of 0.8 minute. If α = 0.05, test the fast food

outletʹs claim using P-values.

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24) A local school district claims that the number of school days missed by its teachers due to illness is below the

national average of μ = 5. A random sample of 28 teachers provided the data below. At α = 0.05, test the

districtʹs claim using P-values.

0 3 6 3 3 5 4 1 3 5

7 3 1 2 3 3 2 4 1 6

2 5 2 8 3 1 2 5

7.4 Hypothesis Testing for Proportions

1 Test a Claim About a Proportion

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.

1) Determine whether the normal sampling distribution can be used. The claim is p < 0.25 and the sample size is

n = 18.

A) Do not use the normal distribution. B) Use the normal distribution.

2) Determine whether the normal sampling distribution can be used. The claim is p ≥ 0.325 and the sample size is

n = 42.

A) Use the normal distribution. B) Do not use the normal distribution.

3) Determine the critical value, z0, to test the claim about the population proportion p = 0.250 given n = 48

and p ^

= 0.231. Use α = 0.01.

A) ±2.575 B) ±1.96 C) ±1.645 D) ±2.33

4) Determine the standardized test statistic, z, to test the claim about the population proportion p = 0.250 given

n = 48 and p ^

= 0.231. Use α = 0.01.

A) -0.304 B) -1.18 C) -0.23 D) -2.87

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

5) Test the claim about the population proportion p ≠ 0.325 given n = 42 and p ^

= 0.247. Use α = 0.05.

6) Fifty-five percent of registered voters in a congressional district are registered Democrats. The Republican

candidate takes a poll to assess his chances in a two-candidate race. He polls 1200 potential voters and finds

that 621 plan to vote for the Republican candidate. Does the Republican candidate have a chance to win? Use

α = 0.05.

7) An airline claims that the no-show rate for passengers is less than 5%. In a sample of 420 randomly selected

reservations, 19 were no-shows. At α = 0.01, test the airlineʹs claim.

8) A recent study claimed that at least 15% of junior high students are overweight. In a sample of 160 students, 18

were found to be overweight. At α = 0.05, test the claim.

9) A recent study claimed that at least 15% of junior high students are overweight. In a sample of 160 students, 18

were found to be overweight. If α = 0.05, test the claim using P-values.

10) A recent study claimed that at least 15% of junior high students are overweight. In a sample of 160 students, 18

were found to be overweight. If α = 0.05, test the claim using confidence intervals.

11) The engineering school at a major university claims that 20% of its graduates are women. In a graduating class

of 210 students, 58 were women. Does this suggest that the school is believable? Use α = 0.05.

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12) A coin is tossed 1000 times and 570 heads appear. At α = 0.05, test the claim that this is not a biased coin. Does

this suggest the coin is fair?

13) A telephone company claims that 20% of its customers have at least two telephone lines. The company selects a

random sample of 500 customers and finds that 88 have two or more telephone lines. At α = 0.05, does the data

support the claim? Use a P-value.

14) A telephone company claims that 20% of its customers have at least two telephone lines. The company selects

a random sample of 500 customers and finds that 88 have two or more telephone lines. If α = 0.05, test the

companyʹs claim using critical values and rejection regions.

15) A telephone company claims that 20% of its customers have at least two telephone lines. The company selects

a random sample of 500 customers and finds that 88 have two or more telephone lines. If α = 0.05, test the

companyʹs claim using confidence intervals.

16) A coin is tossed 1000 times and 530 heads appear. At α = 0.05, test the claim that this is not a biased coin. Use a

P-value. Does this suggest the coin is fair?

7.5 Hypothesis Testing for Variance and Standard Deviation

1 Find Critical Values

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.

1) Find the critical X2 -values to test the claim σ2 = 4.3 if n = 12 and α = 0.05.

A) 3.816, 21.920 B) 2.603, 26.757 C) 3.053, 24.725 D) 4.575, 19.675

2) Find the critical X2 -value to test the claim σ2 ≥ 1.8 if n = 15 and α = 0.05.

A) 6.571 B) 4.075 C) 4.660 D) 5.629

3) Find the critical X2 -value to test the claim σ2 ≤ 3.2 if n = 20 and α = 0.01.

A) 36.191 B) 27.204 C) 30.144 D) 32.852

4) Find the critical X2 -value to test the claim σ2 > 1.9 if n = 18 and α = 0.01.

A) 33.409 B) 27.587 C) 30.181 D) 35.718

5) Find the critical X2 -value to test the claim σ2 < 5.6 if n = 28 and α = 0.10.

A) 18.114 B) 14.573 C) 16.151 D) 36.741

6) Find the critical X2 -values to test the claim σ2 ≠ 6.8 if n = 10 and α = 0.01.

A) 1.735, 23.589 B) 2.088, 21.666 C) 2.700, 19.023 D) 3.325, 16.919

2 Test Claims About Variances and Standard Deviations

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.

7) Compute the standardized test statistic, X2, to test the claim σ2 = 21.5 if n = 12, s2 = 18, and α = 0.05.

A) 9.209 B) 12.961 C) 18.490 D) 0.492

8) Compute the standardized test statistic, X2, to test the claim σ2 ≥ 14.4 if n = 15, s2 = 12, and α = 0.05.

A) 11.667 B) 8.713 C) 12.823 D) 23.891

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9) Compute the standardized test statistic, X2, to test the claim σ2 ≤ 28.8 if n = 20, s2 = 55.8, and α = 0.01.

A) 36.813 B) 9.322 C) 12.82 D) 33.41

10) Compute the standardized test statistic, X2, to test the claim σ2 > 1.9 if n = 18, s2 = 2.7, and α = 0.01.

A) 24.158 B) 28.175 C) 33.233 D) 43.156

11) Compute the standardized test statistic, X2, to test the claim σ2 < 50.4 if n = 28, s2 = 31.5, and α = 0.10.

A) 16.875 B) 14.324 C) 18.132 D) 21.478

12) Compute the standardized test statistic, X2 to test the claim σ2 ≠ 61.2 if n = 10, s2 = 67.5, and α = 0.01.

A) 9.926 B) 3.276 C) 4.919 D) 12.008

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

13) Test the claim that σ2 = 4.3 if n = 12, s2 = 3.6 and α = 0.05. Assume that the population is normally distributed.

14) Test the claim that σ2 ≥ 1.8 if n = 15, s2 = 1.5, and α = 0.05. Assume that the population is normally distributed.

15) Test the claim that σ2 ≤ 3.2 if n = 20, s2 = 6.2, and α = 0.01. Assume that the population is normally distributed.

16) Test the claim that σ2 > 17.1 if n = 18, s2 = 24.3, and α = 0.01. Assume that the population is normally

distributed.

17) Test the claim that σ2 < 39.2 if n = 28, s2 = 24.5, and α = 0.10. Assume that the population is normally

distributed.

18) Test the claim that σ2 ≠ 6.8 if n = 10, s2 = 7.5, and α = 0.01. Assume that the population is normally distributed.

19) Test the claim that σ = 10.35 if n = 12, s = 9.5, and α = 0.05. Assume that the population is normally distributed.

20) Test the claim that σ ≥ 12.06 if n = 15, s = 10.98, and α = 0.05. Assume that the population is normally

distributed.

21) Test the claim that σ ≤ 1.79 if n = 20, s = 2.49, and α = 0.01. Assume that the population is normally distributed.

22) Test the claim that σ > 5.52 if n = 18, s = 6.56, and α = 0.01. Assume that the population is normally distributed.

23) Test the claim that σ < 4.74 if n = 28, s = 3.74 and α = 0.10. Assume that the population is normally distributed.

24) Test the claim that σ ≠ 10.44 if n = 10, s = 10.96, and α = 0.01. Assume that the population is normally

distributed.

25) Listed below is the number of tickets issued by a local police department. Assuming that the data is normally

distributed, test the claim that the standard deviation for the data is 15 tickets. Use α = 0.01.

70 48 41 68 69 55 70

57 60 83 32 60 72 58

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26) The heights (in inches) of 20 randomly selected adult males are listed below. Test the claim that the variance is

less than 6.25. Use α = 0.05. Assume the population is normally distributed.

70 72 71 70 69 73 69 68 70 71

67 71 70 74 69 68 71 71 71 72

27) The heights (in inches) of 20 randomly selected adult males are listed below. Test the claim that the variance is

less than 6.25. Assume the population is normally distributed. Use α = 0.05 and confidence intervals.

70 72 71 70 69 73 69 68 70 71

67 71 70 74 69 68 71 71 71 72

28) A trucking firm suspects that the variance for a certain tire is greater than 1,000,000. To check the claim, the

firm puts 101 of these tires on its trucks and gets a standard deviation of 1200 miles. At α = 0.05, test the

trucking firmʹs claim.

29) A trucking firm suspects that the variance for a certain tire is greater than 1,000,000. To check the claim, the

firm puts 101 of these tires on its trucks and gets a standard deviation of 1200 miles. If α = 0.05, test the

trucking firmʹs claim using confidence intervals.

30) A local bank needs information concerning the standard deviation of the checking account balances of its

customers. From previous information it was assumed to be $250. A random sample of 61 accounts was

checked. The standard deviation was $286.20. At α = 0.01, test the bankʹs assumption. Assume that the account

balances are normally distributed.

31) In one area, monthly incomes of college graduates have a standard deviation of $650. It is believed that the

standard deviation of monthly incomes of non-college graduates is higher. A sample of 71 non-college

graduates are randomly selected and found to have a standard deviation of $950. Test the claim that

non-college graduates have a higher standard deviation. Use α = 0.05.

32) A statistics professor at an all-womenʹs college determined that the standard deviation of womenʹs heights is

2.5 inches. The professor then randomly selected 41 male students from a nearby all-male college and found

the standard deviation to be 2.9 inches. Test the professorʹs claim that the standard deviation of male heights is

greater than 2.5 inches. Use α = 0.01.

3 Test Claims About Variances and Standard Deviations Using a P -value

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

33) The heights (in inches) of 20 randomly selected adult males are listed below. Test the claim that the variance is

less than 6.25. Assume the population is normally distributed. Use α = 0.05 and P-values.

70 72 71 70 69 73 69 68 70 71

67 71 70 74 69 68 71 71 71 72

34) A trucking firm suspects that the variance for a certain tire is greater than 1,000,000. To check the claim, the

firm puts 101 of these tires on its trucks and gets a standard deviation of 1200 miles. If α = 0.05, test the

trucking firmʹs claim using P-values.

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Ch. 7 Hypothesis Testing with One Sample

Answer Key

7.1 Introduction to Hypothesis Testing

1 State a Null and Alternative Hypothesis

1) H0: μ = 48.5, Ha: μ ≠ 48.5

2) H0: μ ≤ 110, Ha: μ > 110

3) H0: μ ≥ 101, Ha: μ < 101

4) H0: p ≥ 0.5, Ha: p < 0.5

5) H0: μ ≤ 4.9, Ha: μ > 4.9

6) H0: σ ≤ 1, Ha: σ > 1

7) claim: μ = 53.7; H0: μ = 53.7, Ha: μ ≠ 53.7; claim is H0

8) claim: μ > 120; H0: μ ≤ 120, Ha: μ > 120; claim is Ha

9) claim: μ < 101; H0: μ ≥ 101, Ha: μ < 101; claim is Ha

10) claim: p ≥ 0.5; H0: p ≥ 0.5, Ha: p < 0.5; claim is H0

11) claim: μ ≤ 3.3; H0: μ ≤ 3.3, Ha: μ > 3.3; claim is H0

12) claim: σ > 1; H0: σ ≤ 1, Ha: σ > 1; claim is Ha

2 Identify Whether to Use a One-tailed or Two-tailed Test

13) A

14) A

15) A

16) A

17) A

18) A

19) A

3 Identify Type I and Type II Errors

20) type I: rejecting H0: μ = 52.5 when μ = 52.5

type II: failing to reject H0: μ = 52.5 when μ ≠ 52.5

21) type I: rejecting H0: μ ≤ 120 when μ ≤ 120

type II: failing to reject H0: μ ≤ 120 when μ > 120

22) type I: rejecting H0: μ ≥ 105 when μ ≥ 105

type II: failing to reject H0: μ ≥ 105 when μ < 105

23) type I: rejecting H0: p ≥ 0.5 when p ≥ 0.5

type II: failing to reject H0: p ≥ 0.5 when p < 0.5

4 Interpret a Decision Based on the Results of a Statistical Test

24) A

25) A

26) A

27) A

28) A

29) A

30) A

31) A

32) A

33) A

34) A

35) A

5 Use Confidence Intervals to Make Decisions

36) A

37) A

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6 Concepts

38) A

39) A

7.2 Hypothesis Testing for the Mean (Large Samples)

1 Find P-values

1) A

2) A

3) A

4) A

2 Test a Claim About a Mean Using P-values

5) A

6) A

7) A

8) Fail to reject H0; There is not enough evidence to support the fast food outletʹs claim that the mean waiting time is less

than 3.4 minutes.

9) P-value = 0.000001, P < α, reject H0; There is sufficient evidence to support the school districtʹs claim.

3 Find Critical Values

10) A

11) A

12) A

13) A

14) A

15) A

4 Test a Claim About a Mean

16) A

17) A

18) A

19) A

20) A

21) A

22) A

23) standardized test statistic ≈ 1.77; critical value = 1.645; reject H0; There is enough evidence to support the claim.

24) standardized test statistic ≈ -1.97; critical value = ±1.96; reject H0; There is enough evidence to support the claim.

25) standardized test statistic ≈ 2.65; critical value = 2.33; reject H0. There is enough evidence to reject the claim.

26) standardized test statistic ≈ -2.16, critical value = ±2.575, fail to reject H0; There is not enough evidence to reject the

claim.

27) standardized test statistic ≈ -3.03; critical value z0 = -2.33; reject H0; The data support the agencyʹs claim.

28) standardized test statistic ≈ -1.58; critical value z0 = ±1.96; fail to reject H0; There is not sufficient evidence to reject

the manufacturerʹs claim.

29) standardized test statistic ≈ -3.74; critical value z0 = -1.645; reject H0; There is sufficient evidence to support the

trucking firmʹs claim.

30) standardized test statistic ≈ -3.58; critical value z0 = -1.645; reject H0; There is sufficient evidence to support the

politicianʹs claim.

31) x = 60.4, s = 12.2, standardized test statistic ≈ 0.18; critical value z0 = 2.33; fail to reject H0; There is not sufficient

evidence to reject the claim.

32) Standardized test statistic ≈ 1.29; critical value z0 = -1.645; fail to reject H0; There is not enough evidence to support

the fast food outletʹs claim.

33) Confidence interval (3.47, 3.73); 3.5 lies in the interval, fail to reject H0; There is not enough evidence to support the

fast food outletʹs claim.

34) Standardized test statistic ≈ -4.71; critical value z0 = -1.645; reject H0; There is sufficient evidence to support the

districtʹs claim.

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35) Confidence interval (2.84, 3.96); 5 lies outside the interval, reject H0; There is sufficient evidence to support the

districtʹs claim.

7.3 Hypothesis Testing for the Mean (Small Samples)

1 Find Critical Values in a t-distribution

1) A

2 Test a Claim About a Mean

2) A

3) A

4) A

5) A

6) A

7) A

8) t0 = ±3.106, standardized test statistic ≈ 1.890, fail to reject H0; There is not sufficient evidence to reject the claim.

9) t0 = -1.833, standardized test statistic ≈ -2.189, reject H0; There is sufficient evidence to reject the claim

10) t0 = 1.761, standardized test statistic ≈ 1.452, fail to reject H0; There is not sufficient evidence to reject the claim

11) t0 = -1.328, standardized test statistic ≈ -0.894, fail to reject H0; There is not sufficient evidence to support the claim

12) t0 = 2.797, standardized test statistic ≈ 1.667, fail to reject H0; There is not sufficient evidence to support the claim

13) t0 = ±3.106, standardized test statistic ≈ -0.825, fail to reject H0; There is not sufficient evidence to support the claim

14) critical value t0 = -2.539; standardized test statistic ≈ -2.981; reject H0; There is sufficient evidence to support the

Metropolitan Bus Companyʹs claim.

15) critical value t0 = -2.539; standardized test statistic ≈ -1.917; fail to reject H0; There is not sufficient evidence to

support the government agencyʹs claim.

16) x = 60.21, s = 13.43; critical value t0 = 2.650; standardized test statistic ≈ 0.060; fail to reject H0; There is not sufficient

evidence to support the claim.

17) Confidence interval (50.70, 69.73); 60 lies in the interval, fail to reject H0; There is not sufficient evidence to reject the

groupʹs claim.

18) critical value t0 = ±2.064; standardized test statistic ≈ -1.875; fail to reject H0; There is not sufficient evidence to reject

the manufacturerʹs claim.

19) Confidence interval (946.98, 1013.02); 1000 lies in the interval, fail to reject H0; There is not sufficient evidence to reject

the manufacturerʹs claim.

20) critical value t0 = -1.740; standardized test statistic -2.121; reject H0; There is sufficient evidence to support the

trucking firmʹs claim.

3 Test a Claim About a Mean Using a P-value

21) P-value = 0.4766. Since the P-value is great than α, there is not sufficient evidence to support the the groupʹs claim.

22) Standardized test statistic ≈ -1.25; Therefore, at a degree of freedom of 24, P must be between 0.10 and 0.25. P > α, fail

to reject H0; There is not sufficient evidence to reject the manufacturerʹs claim.

23) Standardized test statistic ≈ -1.118; Therefore, at 19 degrees of freedom, P must lie between 0.10 and 0.25. Since P > α,

fail to reject H0. There is not sufficient evidence to support the fast food outletʹs claim.

24) standardized test statistic ≈ -4.522; Therefore, at a degree of freedom of 27, P must lie between 0.0001 and 0.00003. P <

α, reject H0. There is sufficient evidence to support the school districtʹs claim.

7.4 Hypothesis Testing for Proportions

1 Test a Claim About a Proportion

1) A

2) A

3) A

4) A

5) critical value z0 = ±1.96; standardized test statistic ≈ -1.08; fail to reject H0; There is not sufficient evidence to support

the claim.

6) critical value z0 = 1.645; standardized test statistic ≈ 1.21; fail to reject H0; There is not sufficient evidence to support

the claim p > 0.5. The Republican candidate has no chance.

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7) critical value z0 = -2.33; standardized test statistic ≈ -0.45; fail to reject H0; There is not sufficient evidence to support

the airlineʹs claim.

8) critical value z0 = -1.645; standardized test statistic ≈ -1.33; fail to reject H0; There is not sufficient evidence to reject

the claim.

9) α = 0.05; P-value = 0.0918; P > α, fail to reject H0; There is not sufficient evidence to reject the studyʹs claim.

10) Confidence interval (0.071, 0.154); 15% lies in the interval, fail to reject H0; There is not sufficient evidence to reject the

studyʹs claim.

11) critical value z0 = ±1.96; standardized test statistic ≈ 2.76; reject H0; There is enough evidence to reject the universityʹs

claim. The school is not believable.

12) critical value z0 = ±1.96; standardized test statistic ≈ 4.43; reject H0; There is enough evidence to reject the claim that

this is not a biased coin. The coin is not fair.

13) α = 0.05; P-value = 0.0901; P > α; fail to reject H0; There is not sufficient evidence to reject the telephone companyʹs

claim.

14) Standardized test statistic ≈ -1.34; critical value z0 = ±1.96; fail to reject H0; There is not sufficient evidence to reject

the companyʹs claim.

15) Confidence interval (0.143, 0.209); 20% lies in the interval, fail to reject H0; There is not sufficient evidence to reject the

companyʹs claim.

16) α = 0.05; P-value = 0.0574; P > α; fail to reject H0; There is not enough evidence to reject the claim that this is not a

biased coin. The coin is fair.

7.5 Hypothesis Testing for Variance and Standard Deviation

1 Find Critical Values

1) A

2) A

3) A

4) A

5) A

6) A

2 Test Claims About Variances and Standard Deviations

7) A

8) A

9) A

10) A

11) A

12) A

13) critical values X 2

L = 3.816 and X 2

R = 21.920; standardized test statistic X2 = 9.209; fail to reject H0; There is not

sufficient evidence to reject the claim.

14) critical value X 20

= 6.571; standardized test statistic X2 ≈ 11.667; fail to reject H0; There is not sufficient evidence to

reject the claim.

15) critical value X 20

= 36.191; standardized test statistic X2 ≈ 36.813; reject H0; There is sufficient evidence to reject the

claim.

16) critical value X 20

= 33.409; standardized test statistic X2 ≈ 24.158; fail to reject H0; There is not sufficient evidence to

reject the claim.

17) critical value X 20

= 18.114; standardized test statistic X2 ≈ 16.875; reject H0; There is sufficient evidence to support the

claim.

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18) critical values X 2

L = 1.735 and X 2

R = 23.589; standardized test statistic X2 ≈ 9.926; fail to reject H0; There is not

sufficient evidence to support the claim.

19) critical values X 2

L = 3.816 and X 2

R = 21.920; standardized test statistic X2 ≈ 9.267; fail to reject H0; There is not

sufficient evidence to reject the claim.

20) critical value X 20

= 6.571; standardized test statistic X2 ≈ 11.605; fail to reject H0; There is not sufficient evidence to

reject the claim.

21) critical value X 20

= 36.191; standardized test statistic X2 ≈ 36.766; reject H0; There is sufficient evidence to reject the

claim.

22) critical value X 20

= 33.409; standardized test statistic X2 ≈ 24.009; fail to reject H0; There is not sufficient evidence to

support the claim.

23) critical value X 20

= 18.114; standardized test statistic X2 ≈ 16.809; reject H0; There is sufficient evidence to support the

claim.

24) critical values X 2

L = 1.735 and X 2

R = 23.589; standardized test statistic X2 ≈ 9.919; fail to reject H0; There is not

sufficient evidence to support the claim.

25) critical values X 2

L = 3.565 and X 2

R = 29.819; standardized test statistic X2 ≈ 10.42; fail to reject H0; There is not

sufficient evidence to reject the claim.

26) critical value X 20

= 10.117; standardized test statistic X2 ≈ 9.048; reject H0; There is sufficient evidence to support the

claim.

27) Confidence interval (1.89, 5.62); 6.25 lies outside the interval, reject H0; There is sufficient evidence to support the

claim.

28) critical value X 20

= 124.342; standardized test statistic X2 = 144; reject H0; There is sufficient evidence to support the

claim.

29) Confidence interval (1,847,835, 1,940,125); 1,000,000 lies outside the interval, reject H0; There is sufficient evidence to

support the claim.

30) critical values X 2

L = 35.534 and X 2

R = 91.952; standardized test statistic X2 ≈ 78.634; fail to reject H0; There is not

sufficient evidence to reject the claim.

31) critical value X 20

= 90.531; standardized test statistics X2 = 149.527; reject H0; There is sufficient evidence to support

the claim.

32) critical value X 20

= 63.691; standardized test statistic X2 = 53.824; fail to reject H0; There is not sufficient evidence to

support the claim.

3 Test Claims About Variances and Standard Deviations Using a P -value

33) Standardized test statistic ≈ 9.048; Therefore, at a degree of freedom of 19, P must be between 0.025 and 0.05. P < α,

reject H0; There is sufficient evidence to support the claim.

34) Standardized test statistic ≈ 144; Therefore, at a degree of freedom of 100, P must be less than 0.005. P < α, reject H0;

There is sufficient evidence to support the firmʹs claim.

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