A+ Answers




Question 1

A long-distance telephone company claims that the mean duration of long-distance telephone

calls originating in one town was greater than 9.4 minutes, which is the average for the state.
Determine the conclusion of the hypothesis test assuming that the results of the sampling do not

lead to rejection of the null hypothesis.

A. Conclusion: Support the claim that the mean is less than 9.4 minutes.

B. Conclusion: Support the claim that the mean is greater than 9.4 minutes.

C. Conclusion: Support the claim that the mean is equal to 9.4 minutes.

D. Conclusion: Do not support the claim that the mean is greater than 9.4 minutes.

A two-tailed test is conducted at the 5% significance level. What is the P-value required to reject

Question 2

the null hypothesis?

A. Greater than or equal to 0.10

B. Less than or equal to 0.05

C. Less than or equal to 0.10

D. Greater than or equal to 0.05

A nationwide study of American homeowners revealed that 65% have one or more lawn mowers.

Question 3

A lawn equipment manufacturer, located in Omaha, feels the estimate is too low for households

in Omaha. Find the P-value for a test of the claim that the proportion with lawn mowers in

Omaha is higher than 65%. Among 497 randomly selected homes in Omaha, 340 had one or more

lawn mowers. Use Table 5.1 to find the best answer.

A. 0.0559

B. 0.1118

C. 0.0252

D. 0.0505

Question 4

The principal of a middle school claims that annual incomes of the families of the seventhgraders

at his school vary more than the annual incomes of the families of the seventh graders at a

neighboring school, which have variation described by = $13,700.

Assume that a hypothesis test of the claim has been conducted and that the conclusion of the test

was to reject the null hypothesis.

Identify the population to which the results of the test apply.

A. The current seventh graders at the principal’s school

B. Seventh graders’ families at the school with a standard deviation of $13,700

C. All of the families of the class of seventh graders at the principal’s school

D. All seventh graders’ families

Question 5

 A researcher wants to check the claim that convicted burglars spend an average of 18.7 months

in jail. She takes a random sample of 35 such cases from court files and finds that months. Assume that the population standard deviation is 7 months. Test the null hypothesis that µ = 18.7 at the 0.05 significance level.

A. Do not reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months is supported.

B. Do not reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months cannot be supported.

C. Reject the null hypothesis and conclude that the claim that the mean is different from 18.7

months is supported.

D. Reject the null hypothesis and conclude that the claim that the mean is different from 18.7

months cannot be supported.

Question 6

In the past, the mean running time for a certain type of flashlight battery has been 9.8 hours. The

manufacturer has introduced a change in the production method and wants to perform a

hypothesis test to determine whether the mean running time has increased as a result. The

hypotheses are:

Suppose that the results of the sampling lead to rejection of the null hypothesis. Classify that

conclusion as a Type I error, a Type II error, or a correct decision, if in fact the mean running

time has not increased.

A. Type I error

B. Type II error

C. Correct decision

D. Can not be determined from this information

Question 7

A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO

is less than 1 in every one thousand. State the null hypothesis and the alternative hypothesis for a

test of significance.

Question

A right-tailed test is conducted at the 5% significance level. Which of the following z-scores is

the smallest one in absolute value that leads to rejection of the null hypothesis? 

A. 1.61

B. 1.85

C. -1.98

D. -2.06

Question 9

A study of a brand of “in the shell peanuts” gives the following results:

A significant event at the 0.01 level is a fan getting a bag with how many peanuts?

A. 30 peanuts

B. 25 or 30 peanuts

C. 25 or 55 peanuts

D. 25 peanuts

A psychologist claims that more than 19 percent of the population suffers from professional

Question 10

problems due to extreme shyness. Assume that a hypothesis test of the claim has been conducted

and that the conclusion of the test was to reject the null hypothesis. Identify the population to

which the results of the test apply.

A. The population is all shy workers.

B. The population cannot be identified from the description of the study.

C. The population is all American workers.

D. The population is all American professional workers (doctors, lawyers, CPA’s, and the like..

Question 11

A consumer group claims that the mean running time for a certain type of flashlight battery is not

the same as the manufacturer’s claims. Determine the null and alternative hypotheses for the test

described.

In 1990, the average duration of long-distance telephone calls originating in one town was 9.4

minutes. A long-distance telephone company wants to perform a hypothesis test to determine

whether the average duration of long-distance phone calls has changed from the 1990 mean of 9.4

minutes. The mean duration for a random sample of 50 calls originating in the town was 8.6

minutes. Does the data provide sufficient evidence to conclude that the mean call duration, µ, is

different from the 1990 mean of 9.4 minutes? Perform the appropriate hypothesis test using a

significance level of 0.01. Assume that = 4.8 minutes.

A. With a z of -1.2 there is sufficient evidence to conclude that the mean value has changed from the 1990 mean of 9.4 minutes.

B. With a P-value of 0.2302 there is not sufficient evidence to conclude that the mean value is less than the 1990 mean of 9.4 minutes.

C. With a P-value of 0.2302 there is sufficient evidence to conclude that the mean value is less than the 1990 mean of 9.4 minutes.

D. With a z of –1.2 there is not sufficient evidence to conclude that the mean value has changed from the 1990 mean of 9.4 minutes.

Question 13

If a fan purchased a bag with 30 peanuts, what is the lowest level at which this would be a

significant event?

A. 0.05

B. 0.025

C. 0.01

D. It is not significant at any of the levels given

The owner of a football team claims that the average attendance at home games is over 3000, and

Question 14

he is therefore justified in moving the team to a city with a larger stadium. Assuming that a

hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null

hypothesis, state the conclusion in non-technical terms.

A. There is sufficient evidence to support the claim that the mean attendance is greater than

3000.

B. There is sufficient evidence to support the claim that the mean attendance is equal to 3000.

C. There is not sufficient evidence to support the claim that the mean attendance is greater than

3000.

D. There is not sufficient evidence to support the claim that the mean attendance is less than

3000.

Question 15

A manufacturer claims that the mean amount of juice in its 16 ounce bottles is 16.1 ounces. A

consumer advocacy group wants to perform a hypothesis test to determine whether the mean

amount is actually less than this. The mean volume of juice for a random sample of 70 bottles

was 15.94 ounces. Do the data provide sufficient evidence to conclude that the mean amount of

juice for all 16-ounce bottles, µ, is less than 16.1 ounces? Perform the appropriate hypothesis test

using a significance level of 0.10. Assume that  = 0.9 ounces. 

A. The z of  1.49 provides sufficient evidence to conclude that the mean amount of juice is less than 16.1 oz.

B. The z of  1.49 does not provide sufficient evidence to conclude that the mean amount of juice is less than 16.1 oz.

C. The z of  0.1778 does not provide sufficient evidence to conclude that the mean amount of juice is less than 16.1 oz.

D. The z of  0.1778 provides sufficient evidence to conclude that the mean amount of juice is less than 16.1 oz.

A psychologist claims that more than 29 percent of the professional population suffers from

Question 16

problems due to extreme shyness. Assuming that a hypothesis test of the claim has been

conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in

non-technical terms.

A. There is sufficient evidence to support the claim that the true proportion is less than 29

percent.

B. There is not sufficient evidence to support the claim that the true proportion is greater than 29

percent.

C. There is sufficient evidence to support the claim that the true proportion is equal to 29 percent.

D. There is sufficient evidence to support the claim that the true proportion is greater than 29

percent.

The owner of a football team claims that the average attendance at home games is over 4000, and

Question 17

he is therefore justified in moving the team to a city with a larger stadium. Assume that a

hypothesis test of the claim has been conducted and that the conclusion of the test was to reject

the null hypothesis. Identify the population to which the results of the test apply.

A. All games played by the team in question in which the attendance is over 4000

B. All future home games to be played by the team in question

C. All home games played by the team in question

D. None of the populations given are appropriate

Question 18

without computing a P-value, determine whether the alternate hypothesis is supported and give a

reason for your conclusion.

is less than 1 standard deviation above the claimed mean.

is more than 4 standard deviations above the claimed mean.

is less than 1 standard deviation above the claimed mean.

is more than 4 standard deviations above the claimed mean.

Question 19

At one school, the mean amount of time that tenth-graders spend watching television each week

is 18.4 hours. The principal introduces a campaign to encourage the students to watch less

television. One year later, the principal wants to perform a hypothesis test to determine whether

the average amount of time spent watching television per week has decreased.

Formulate the null and alternative hypotheses for the study described.

Question 21

Which of the following statements is true?

A. The t distribution can be used when finding a confidence interval for the population mean

whenever the sample size is small.

B. The p distribution can be used when finding a confidence interval for the population mean

whenever the sample size is small.

C. The t distribution cannot be used when finding a confidence interval for the population mean

whenever the sample size is small.

D. The p distribution cannot be used when finding a confidence interval for the sample mean

whenever the sample size is small.

Question 22

A 95% confidence interval for the mean of a normal population is found to be 15.6 < µ < 24.8.

What is the margin of error?

A. 4.4

B. 4.6

C. 4.8

D. 5.0

The __________ test statistic is for the one-way analysis of variance.

Question 23

A. P-Value

B. t

C. F

D. p

Question 24

A simple random sample from a normal distribution is taken in order to obtain a 95% confidence

interval for the population mean. If the sample size is 8, the sample mean x is 22, and the sample

standard deviation s is 6.3, what is the margin of error? Show your answer to 2 decimal places.

A. df = 7; E = 3.3445.38 = 5.6566

B. df = 8; E = 3.3445.38 = 5.6566

C. df = 6; E = 2.3656.38 = 5.769

D. df = 7; E = 2.3656.38 = 5.869

Question 25

One hundred people are selected at random and tested for colorblindness to determine whether

gender and colorblindness are independent. The following counts were observed.

Colorblind Not Colorblind Total

Male 7 53 60

Female 1 39 40

Total 8 92 100

Find the value of the X

A. 1.325

B. 1.318

C. 1.286

D. 1.264

Question 26

A 95% confidence interval for the mean of a normal population is found to be 13.2 < µ < 22.4.

What is the margin of error?

A. 4.6

B. 4.4

C. 4.2

D. 5.6

Question 27

A golfer wished to find a ball that would travel more than 170 yards when hit with his 6-iron with a club head speed of 90 miles per hour. He had a golf equipment lab test a low compression ball by having a robot swing his club 12 times at the required speed.

Data from this test had a sample mean of 171.6 yards with a sample standard deviation of 2.4

yards. Assuming normality, carry out a hypothesis test at the 0.05 significance level to determine

whether the ball meets the golfer’s requirements. Use the partial t-table below.

Area in one tail

Area in two tails

Degrees of

Freedom

Accept the null hypothesis. The data do not provide sufficient evidence that the average distance

is greater than 170 yards.

B. Accept the null hypothesis. The data do provide sufficient evidence that the average distance

is greater than 170 yards.

C. Reject the null hypothesis. The data do not provide sufficient evidence that the average

distance is greater than 170 yards.

D. Reject the null hypothesis. The data do provide sufficient evidence that the average distance is

greater than 170 yards.

Question 28

One hundred people are selected at random and tested for colorblindness to determine whether

gender and colorblindness are independent.

The critical value of X 2 for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of

the X 2 statistic is 3.179, state your conclusion about the relationship between gender and

colorblindness..

There is sufficient evidence to support the claim that gender and colorblindness are not related.

D. There is not sufficient evidence to accept or reject H

Question 29

A golfer wished to find a ball that would travel more than 170 yards when hit with his 6-iron with a club head speed of 90 miles per hour. He had a golf equipment lab test a low compression ball by having a robot swing his club 12 times at the required speed. State the null and alternative

hypotheses for this test.

Question 30

The following data were analyzed using one-way analysis of variance.

A B C

34 27 19

26 23 21

31 29 22

28 21 12

Which one of the following statements is correct?

A. The purpose of the analysis is to determine whether the groups A, B, and C are independent.

B. The purpose of the analysis is to test the hypothesis that the population means of the three

groups are equal.

C. The purpose of the analysis is to test the hypothesis that the population variances of the three

groups are equal.

D. The purpose of the analysis is to test the hypothesis that the sample means of the three groups

are equal.

Question 31

One hundred people are selected at random and tested for colorblindness to determine whether

gender and colorblindness are independent. The following counts were observed.

Colorblind Not Colorblind Total

Male 7 53 60

Female 1 39 40

Total 8 92 100

If gender and colorblindness are independent, find the expected values corresponding to the male

combinations of gender and colorblindness.

A. Colorblind Male 4.8; Not Colorblind Male 55.2

B. Colorblind Male 6.8; Not Colorblind Male 53.2

C. Colorblind Male 4.8; Not Colorblind Male 55.4

D. Colorblind Male 4.8; Not Colorblind Male 56.2

Question 32

A golfer wished to find a ball that would travel more than 180 yards when hit with his 5-iron with a club speed of 90 miles per hour. He had a golf equipment lab test a low compression ball by having a robot swing his club 7 times at the required speed.

Data from this test resulted in a sample mean of 184.2 yards and a sample standard deviation of

5.8 yards. Assuming normality, carry out a hypothesis test at the 0.05 significance level to

determine whether the ball meets the golfer’s requirements. Use the partial t-table below.

A.

Reject the null hypothesis. The data do not provide sufficient evidence that the average distance

is greater than 180 yards.

B. Reject the null hypothesis. The data do provide sufficient evidence that the average distance is

greater than 180 yards.

C. Do not reject the null hypothesis. The data do provide sufficient evidence that the average

distance is greater than 180 yards.

D. Do not reject the null hypothesis. The data do not provide sufficient evidence that the average

distance is greater than 180 yards.

Question 33

One hundred people are selected at random and tested for colorblindness to determine whether

gender and colorblindness are independent.

The critical value of X 2 for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of

the X 2  statistic is 4.613, state your conclusion about the relationship between gender and

colorblindness.

A. Reject H

There is not sufficient evidence to support the claim that gender and colorblindness

are related.

B. Reject H

There is sufficient evidence to support the claim that gender and colorblindness are

related.

C. Do not Reject H. There is sufficient evidence to support the claim that gender and

colorblindness are related.

D. Do not Reject H. There is not sufficient evidence to support the claim that gender and

colorblindness are related.

Question 34

A 95% confidence interval for the mean of a normal population is found to be 15.6 < µ < 25.2.

What is the margin of error?

A. 3.9

B. 4.8

C. 4.9

D. 3.7

Question 35

One hundred people are selected at random and tested for colorblindness to determine whether

gender and colorblindness are independent. The following counts were observed.

Colorblind

Not

Colorblind

Total

Male 8 52 60

Female 2 38 40

Total 10 90 100

State the null and alternative hypothesis for the test associated with this data.: Colorblindness and gender are related in some way.

Question 36

One hundred people are selected at random and tested for colorblindness to determine whether

gender and colorblindness are independent. The following counts were observed.

Colorblind Not Colorblind Total

Male 7 53 60

Female 1 39 40

Total 8 92 100

State the null and alternative hypothesis for the information above.

Question 37

The margin of error in estimating the population mean of a normal population is E = 9.3 when the

sample size is 15. If the sample size had been 18 and the sample standard deviation did not

change, would the margin of error be larger or smaller than 9.3? Explain your answer.

A. Smaller. E decreases as the square root of the sample size gets larger.

B. Smaller. E increases as the square root of the sample size gets larger.

C. Larger. E decreases as the square root of the sample size gets larger.

D. Larger. E increases as the square root of the sample size gets larger.

Question 38

One hundred people are selected at random and tested for colorblindness to determine whether

gender and colorblindness are independent. The following counts were observed.

Colorblind

Not

Colorblind

Total

Male 8 52 60

Female 2 38 40

Total 10 90 100

Find the value of the X

A. 1.463

2

statistic for the data above.

B. 1.852

C. 1.947

D. 1.949

Question 39

One hundred people are selected at random and tested for colorblindness to determine whether

gender and colorblindness are independent. The following counts were observed.

Colorblind

Not

Colorblind

Total

Male 8 52 60

Female 2 38 40

Total 10 90 100

If gender and colorblindness are independent, find the expected values corresponding to the four

combinations of gender and colorblindness, and enter them in the following table along with row

and column totals.

Colorblind Not Total

Colorblind

Male    

Female    

Total     

A. Male Colorblind 6.0; Male Not Colorblind 54.0

B. Male Colorblind 7.0; Male Not Colorblind 53.0

C. Male Colorblind 8.0; Male Not Colorblind 52.0

D. Male Colorblind 6.0; Male Not Colorblind 53.0

Question 40

Which of the following statements is true?

A. The p distribution cannot be used when finding a confidence interval for the population mean

with a small sample anytime the population standard deviation is unknown.

B. The t distribution can be used when finding a confidence interval for the population mean

with a small sample anytime the population standard deviation is unknown.

C. The t distribution cannot be used when finding a confidence interval for the population mean

with a small sample anytime the population standard deviation is unknown.

D. The p distribution can be used when finding a confidence interval for the population mean

with a small sample anytime the population standard deviation is unknown.