A consumer advocacy group claims that the mean amount of juice in a 16 ounce bottled drink is not 16 ounces, as stated by the bottler. Determine the conclusion of the hypothesis test assuming that the results of the sampling lead to rejection of the null hypothesis.

A. Conclusion: Support the claim that the mean is equal to 16 ounces.

B. Conclusion: Support the claim that the mean is greater than 16 ounces.

C. Conclusion: Support the claim that the mean is not equal to 16 ounces.

D. Conclusion: Support the claim that the mean is less than 16 ounces.

Question 4 of 40

0.0/ 2.5 Points

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.

A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a mean different from the 600 mg claimed by the manufacturer. Test this claim at the 0.02 level of significance. The mean acetaminophen content for a random sample of n = 41 tablets is 603.3 mg. Assume that the population standard deviation is 4.9 mg.

A. Since the test statistic is greater than the critical z, there is sufficient evidence to accept the null hypothesis and to support the claim that the mean content of acetaminophen is 600 mg.

B. Since the test statistic is greater than the critical z, there is sufficient evidence to reject the null hypothesis and to support the claim that the mean content of acetaminophen is not 600 mg.

C. Since the test statistic is less than the critical z, there is sufficient evidence to reject the null hypothesis and to support the claim that the mean content of acetaminophen is not 600 mg.

D. Since the test statistic is greater than the critical z, there is insufficient evidence to reject the null hypothesis and to support the claim that the mean content of acetaminophen is not 600 mg.

Question 6 of 40

0.0/ 2.5 Points

In 1990, the average duration of long-distance telephone calls originating in one town was 9.3 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 9.3 minutes. Formulate the null and alternative hypotheses for the study described.

A.

H_{o}: µ = 9.3 minutes H_{a}: µ < 9.3 minutes

B.

H_{o}: µ = 9.3 minutes H_{a}: µ > 9.3 minutes

C.

H_{o}: µ = 9.3 minutes H_{a}: µ ¹9.3 minutes

D.

H_{o}: µ ¹9.3 minutes H_{a}: µ = 9.3 minutes

Question 7 of 40

2.5/ 2.5 Points

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.

A.

H_{0}: p = 0.001 H_{a}: p > 0.001

B.

H_{0}: p = 0.001 H_{a}: p < 0.001

C.

H_{0}: p > 0.001 H_{a}: p = 0.001

D.

H_{0}: p < 0.001 H_{a}: p = 0.001

Question 8 of 40

0.0/ 2.5 Points

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

Question 9 of 40

0.0/ 2.5 Points

A two-tailed test is conducted at the 5% significance level. What is the left tail percentile required to reject the null hypothesis?

A. 97.5%

B. 5%

C. 2.5%

D. 95%

Question 10 of 40

0.0/ 2.5 Points

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.

A.

H_{o}: µ = 18.4 hours H_{a}: µ ¹18.4 hours

B.

H_{o}: µ = 18.4 hours H_{a}: µ < 18.4 hours

C.

H_{o}: µ ³18.4 hours H_{a}: µ < 18.4 hours

D.

H_{o}: µ = 18.4 hours H_{a}: µ > 18.4 hours

Question 11 of 40

0.0/ 2.5 Points

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 12 of 40

0.0/ 2.5 Points

In the past, the mean running time for a certain type of flashlight battery has been 8.0 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:

H_{0} : µ = 8.0 hours

H_{a} : µ > 8.0 hours

Explain the meaning of a Type II error.

A. Concluding that µ > 8.0 hours when in fact µ > 8.0 hours

B. Failing to reject the hypothesis that µ = 8.0 hours when in fact µ > 8.0 hours

C. Concluding that µ > 8.0 hours

D. Failing to reject the hypothesis that µ = 8.0 hours when in fact µ = 8.0 hours

Question 13 of 40

2.5/ 2.5 Points

A supplier of DVDs claims that no more than 1% of the DVDs are defective. In a random sample of 600 DVDs, it is found that 3% are defective, but the supplier claims that this is only a sample fluctuation. At the 0.01 level of significance, test the supplier’s claim that no more than 1% are defective.

A. Do not reject the null hypothesis and conclude that there is evidence to support the claim that more than 1% of the DVDs are defective.

B. Reject the null hypothesis and conclude that there is insufficient evidence to support the claim that more than 1% of the DVDs are defective.

C. Do not reject the null hypothesis and conclude that there is insufficient evidence to support the claim that more than 1% of the DVDs are defective.

D. Reject the null hypothesis and conclude that there is sufficient evidence to support the claim that more than 1% of the DVDs are defective.

Question 14 of 40

0.0/ 2.5 Points

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

Question 15 of 40

0.0/ 2.5 Points

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.

Question 16 of 40

0.0/ 2.5 Points

The owner of a football team claims that the average attendance at home games is over 3000, and 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 17 of 40

0.0/ 2.5 Points

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:

H_{0} : µ = 9.8 hours

H_{a} : µ > 9.8 hours

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 18 of 40

0.0/ 2.5 Points

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

Question 19 of 40

2.5/ 2.5 Points

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 s = 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.

Question 20 of 40

0.0/ 2.5 Points

A consumer advocacy group claims that the mean amount of juice in a 16 ounce bottled drink is not 16 ounces, as stated by the bottler. Determine the null and alternative hypotheses for the test described.

A.

H_{0}: µ = 16 ounces H_{a}: µ < 16 ounces

B.

H_{0}: µ ¹16 ounces H_{a}: µ = 16 ounces

C.

H_{0}: µ = 16 ounces H_{a}: µ > 16 ounces

D.

H_{0}: µ = 16 ounces H_{a}: µ ¹16 ounces

Part 2 of 2 –

7.5/ 50.0 Points

Question 21 of 40

0.0/ 2.5 Points

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 22 of 40

0.0/ 2.5 Points

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.

A.

H_{0}: µ > 170; H_{a}: µ = 170

B.

H_{0}: µ < 170; H_{a}: µ = 170

C.

H_{0}: µ = 170; H_{a}: µ > 170

D.

H_{0}: µ = 160; H_{a}: µ > 160

Question 23 of 40

0.0/ 2.5 Points

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. State the null and alternative hypotheses for this test.

A.

H_{0}: µ = 180; H_{a}: µ > 180

B.

H_{0}: µ > 180; H_{a}: µ > 180

C.

H_{0}: µ < 180; H_{a}: µ > 180

D.

H_{0}: µ = 180; H_{a}: µ < 180

Question 24 of 40

0.0/ 2.5 Points

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 25 of 40

0.0/ 2.5 Points

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.

Area in one tail

0.025

0.05

Area in two tails

Degrees of Freedom n – 1

0.05

0.10

6

2.447

1.943

7

2.365

1.895

8

2.306

1.860

9

2.262

1.833

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 26 of 40

0.0/ 2.5 Points

A 95% confidence interval for the mean of a normal population is found to be 17.6 < µ < 23.6. What is the margin of error?

A. 2.0

B. 2.7

C. 3.0

D. 4.0

Question 27 of 40

0.0/ 2.5 Points

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.

A.

H_{0}: Colorblindness and gender are dependent characteristics. H_{a}: Colorblindness and gender are related in some way.

B.

H_{0}: Colorblindness and gender are independent characteristics. H_{a}: Colorblindness and gender are not related in any way.

C.

H_{0}: Colorblindness and gender are dependent characteristics. H_{a}: Colorblindness and gender are not related in any way.

D.

H_{0}: Colorblindness and gender are independent characteristics. H_{a}: Colorblindness and gender are related in some way.

Question 28 of 40

0.0/ 2.5 Points

Which of the following statements is true?

A. The t distribution cannot be used when finding a confidence interval for the population mean with a small sample whenever the sample comes from a symmetric population.

B. The t distribution can be used when finding a confidence interval for the population mean with a small sample whenever the sample comes from a symmetric population.

C. The p distribution can be used when finding a confidence interval for the population mean with a small sample whenever the sample comes from a symmetric population.

D. The p distribution can be used when finding a confidence interval for the population mean with a small sample whenever the sample comes from a symmetric population.

Question 29 of 40

0.0/ 2.5 Points

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.

A.

H_{0}: Colorblindness and gender are dependent characteristics. H_{a}: Colorblindness and gender are not related in any way.

B.

H_{0}: Colorblindness and gender are dependent characteristics. H_{a}: Colorblindness and gender are related in some way.

C.

H_{0}: Colorblindness and gender are independent characteristics. H_{a}: Colorblindness and gender are not related in any way.

D.

H_{0}: Colorblindness and gender are independent characteristics. H_{a}: Colorblindness and gender are related in some way.

Question 30 of 40

0.0/ 2.5 Points

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 χ2 statistic for the data above.

A. 1.463

B. 1.852

C. 1.947

D. 1.949

Question 31 of 40

0.0/ 2.5 Points

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 32 of 40

2.5/ 2.5 Points

A golfer wished to find a ball that would travel more than 160 yards when hit with his 7-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 8 times at the required speed.

Data from this test resulted in a sample mean of 163.2 yards with 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 to solve this problem.

Area in one tail

0.025

0.05

Area in two tails

Degrees of Freedom n – 1

0.05

0.10

6

2.447

1.943

7

2.365

1.895

8

2.306

1.860

9

2.262

1.833

A.

Do not reject the null hypothesis. The data do not provide sufficient evidence that the average distance is greater than 160 yards.

B. Reject the null hypothesis. The data does provide sufficient evidence that the average distance is greater than 160 yards.

C. t= 1.2334; Critical value = 1.992

D. Insufficient information to answer this question.

Question 33 of 40

0.0/ 2.5 Points

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 x̄ 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 34 of 40

2.5/ 2.5 Points

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 35 of 40

0.0/ 2.5 Points

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 36 of 40

2.5/ 2.5 Points

The critical value of χ 2 for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of the χ 2 statistic in Problem 8 had been 3.179, state your conclusion about the relationship between gender and colorblindness.

A.

Do not reject H_{0}.

B.

Reject H_{0}.

C.

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_{0}.

Question 37 of 40

0.0/ 2.5 Points

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 χ^{2} statistic for the data above.

A. 1.325

B. 1.318

C. 1.286

D. 1.264

Question 38 of 40

0.0/ 2.5 Points

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

Question 39 of 40

0.0/ 2.5 Points

The critical value of χ2 for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of the χ2 statistic in Problem #21 had been 4.613, state your conclusion about the relationship between gender and colorblindness.

A.

Reject H_{0}. There is not sufficient evidence to support the claim that gender and colorblindness are related.

B.

Reject H_{0}. There is sufficient evidence to support the claim that gender and colorblindness are related.

C.

Do not Reject H_{0}. There is sufficient evidence to support the claim that gender and colorblindness are related.

D.

Do not Reject H_{0}. There is not sufficient evidence to support the claim that gender and colorblindness are related.

Question 40 of 40

0.0/ 2.5 Points

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.

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