# Expert Answers

Question 21

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 H0. There is not sufficient evidence to support the claim that gender and colorblindness are related.

B.

Reject H0. There is sufficient evidence to support the claim that gender and colorblindness are related.

C.

Do not Reject H0. There is sufficient evidence to support the claim that gender and colorblindness are related.

D.

Do not Reject H0. There is not sufficient evidence to support the claim that gender and colorblindness are related.

Question 22 of 40

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.

H0: µ = 180; Ha: µ 180

H0: µ 180; Ha: µ 180

C.H0: µ < 180; Ha: µ 180

H0: µ = 180; Ha: µ < 180

Question 23 of 40

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 24 of 40

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 25 and the sample standard deviation did not change, would the margin of error be larger or smaller than 9.3?

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

B. Smaller. E decreases 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 25 of 40

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 26 of 40

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 27 of 40

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.

H0: Colorblindness and gender are dependent characteristics.

Ha: Colorblindness and gender are related in some way.

B.

H0: Colorblindness and gender are independent characteristics.

Ha: Colorblindness and gender are not related in any way.

C.

H0: Colorblindness and gender are dependent characteristics.

Ha: Colorblindness and gender are not related in any way.

D.

H0: Colorblindness and gender are independent characteristics.

Ha: Colorblindness and gender are related in some way.

Question 28 of 40

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

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.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 29 of 40

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 30 of 40

A large test statistic F tells us that the sample means __________ the data within the individual samples, which would be unlikely if the populations means really were equal (as the null hypothesis claims).

A. differ more than

B. differ less than

C. are equal to

D. do not vary with

Question 31 of 40

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.

Do not reject H0.

B. Reject H0.

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 H0.

Question 32 of 40

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 33 of 40

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 χ2 statistic for the data above.

A. 1.325

B. 1.318

C. 1.286 D. 1.264

Question 34 of 40

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 35 of 40

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.

H0: µ 170; Ha: µ = 170

H0: µ < 170; Ha: µ = 170

H0: µ = 170; Ha: µ 170

H0: µ = 160; Ha: µ 160Question 36 of 40

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

A B C

34 27 19

26 23 31

31 29 22

28 21 22

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 37 of 40

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. State the null and alternative hypotheses for this test.

A.H0: µ = 160; Ha: µ 150

B.H0: µ = 150; Ha: µ 150

C.H0: µ = 160; Ha: µ 160

D.H0: µ = 140; Ha: µ 160

Question 38 of 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.

Question 39 of 40

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 Colorblind Total

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

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.

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 H0. There is not sufficient evidence to support the claim that gender and colorblindness are related.

B.

Reject H0. There is sufficient evidence to support the claim that gender and colorblindness are related.

C.

Do not Reject H0. There is sufficient evidence to support the claim that gender and colorblindness are related.

D.

Do not Reject H0. There is not sufficient evidence to support the claim that gender and colorblindness are related.

Question 22 of 40

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.

H0: µ = 180; Ha: µ 180

H0: µ 180; Ha: µ 180

C.H0: µ < 180; Ha: µ 180

H0: µ = 180; Ha: µ < 180

Question 23 of 40

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 24 of 40

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 25 and the sample standard deviation did not change, would the margin of error be larger or smaller than 9.3?

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

B. Smaller. E decreases 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 25 of 40

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 26 of 40

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 27 of 40

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.

H0: Colorblindness and gender are dependent characteristics.

Ha: Colorblindness and gender are related in some way.

B.

H0: Colorblindness and gender are independent characteristics.

Ha: Colorblindness and gender are not related in any way.

C.

H0: Colorblindness and gender are dependent characteristics.

Ha: Colorblindness and gender are not related in any way.

D.

H0: Colorblindness and gender are independent characteristics.

Ha: Colorblindness and gender are related in some way.

Question 28 of 40

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

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.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 29 of 40

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 30 of 40

A large test statistic F tells us that the sample means __________ the data within the individual samples, which would be unlikely if the populations means really were equal (as the null hypothesis claims).

A. differ more than

B. differ less than

C. are equal to

D. do not vary with

Question 31 of 40

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.

Do not reject H0.

B. Reject H0.

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 H0.

Question 32 of 40

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 33 of 40

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 χ2 statistic for the data above.

A. 1.325

B. 1.318

C. 1.286 D. 1.264

Question 34 of 40

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 35 of 40

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.

H0: µ 170; Ha: µ = 170

H0: µ < 170; Ha: µ = 170

H0: µ = 170; Ha: µ 170

H0: µ = 160; Ha: µ 160Question 36 of 40

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

A B C

34 27 19

26 23 31

31 29 22

28 21 22

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 37 of 40

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. State the null and alternative hypotheses for this test.

A.H0: µ = 160; Ha: µ 150

B.H0: µ = 150; Ha: µ 150

C.H0: µ = 160; Ha: µ 160

D.H0: µ = 140; Ha: µ 160

Question 38 of 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.

Question 39 of 40

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 Colorblind Total

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

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.

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