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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.


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.


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.


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.


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



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


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 youinterpret 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.


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 5.1years. 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



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



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



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


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


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



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


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



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



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


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


A) ±1.81 B) ±2.33 C) ±2.575 D) ±1.96

4 Test a Claim About a Mean



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,


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,


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 ofα = 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.


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 8332 60 72 58 88 48 59 60 56 65

66 60 68 42 57 59 49 70 75 63

44


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.


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


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) 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. Roundyour 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


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


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


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


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


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


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




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


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.


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



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


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.


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


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



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



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


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


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 7167 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.


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 itscustomers. 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 isgreater than 2.5 inches. Use α = 0.01.

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




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


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 SampleAnswer Key

7.1 Introduction to Hypothesis Testing1 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 < 0.55) 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) A14) 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) A31) 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) A14) A

15) A


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) A

3) A

4) A5) 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


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


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

Proportion1) 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 Deviation1 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) A11) A

12) A

13) critical values X 2L = 3.816 and X

2R = 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.


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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2R = 23.589; standardized test statistic X2 ≈ 9.926; fail to reject H0; There is not

sufficient evidence to support the claim.





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.


support the claim.


claim.



sufficient evidence to support the claim.





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.




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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