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Question: 5. A small company decides to offer a new online shopping feature. The company's president wants to offer a free gift card to customers

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5. A small company decides to offer a new online shopping feature. The company's president wants to offer a free gift card to customers who make a $200 minimum purchase online. These customers can choose any one of three different gift cards of equal value. A month after starting this promotion, it is found that 40 customers selected a restaurant gift card, 29 of them selected a grocery store gift card, and 33 of them selected a movie theater gift card. Using a significance level of 0.05, test the claim that the three gift cards being offered in this promotion are equally popular.

Identify the CONCLUSION of a hypothesis test of the claim.

There is sufficient evidence to warrant rejection of the claim.

There is not sufficient evidence to warrant rejection of the claim.

There is not sufficient evidence to support the claim.

There is sufficient evidence to support the claim.

6. A small company decides to offer a new online shopping feature. The company's president wants to offer a free gift card to customers who make a $200 minimum purchase online. These customers can choose any one of three different gift cards of equal value. A month after starting this promotion, it is found that 40 customers selected a restaurant gift card, 29 of them selected a grocery store gift card, and 33 of them selected a movie theater gift card. Using a significance level of 0.05, test the claim that the three gift cards being offered in this promotion are equally popular.

Find the value of the P-VALUE that would be used in a hypothesis test of the claim.

0.408

0.610

0.402

0.617

7. A small company decides to offer a new online shopping feature. The company's president wants to offer a free gift card to customers who make a $200 minimum purchase online. These customers can choose any one of three different gift cards of equal value. A month after starting this promotion, it is found that 40 customers selected a restaurant gift card, 29 of them selected a grocery store gift card, and 33 of them selected a movie theater gift card. Using a significance level of 0.05, test the claim that the three gift cards being offered in this promotion are equally popular.

Identify the absolute value of the CRITICAL VALUE used in a hypothesis test of the claim.

5.991

7.815

9.348

7.378

8. A small company decides to offer a new online shopping feature. The company's president wants to offer a free gift card to customers who make a $200 minimum purchase online. These customers can choose any one of three different gift cards of equal value. A month after starting this promotion, it is found that 40 customers selected a restaurant gift card, 29 of them selected a grocery store gift card, and 33 of them selected a movie theater gift card. Using a significance level of 0.05, test the claim that the three gift cards being offered in this promotion are equally popular.

Identify the value of the TEST STATISTIC used in a hypothesis test of the claim.

1.792

1.824

9. A small company decides to offer a new online shopping feature. The company's president wants to offer a free gift card to customers who make a $200 minimum purchase online. These customers can choose any one of three different gift cards of equal value. A month after starting this promotion, it is found that 40 customers selected a restaurant gift card, 29 of them selected a grocery store gift card, and 33 of them selected a movie theater gift card. Using a significance level of 0.05, test the claim that the three gift cards being offered in this promotion are equally popular.

Identify the correct HYPOTHESES used in a hypothesis test of the claim.

H0: prestaurant = 40, pgrocery = 29, pmovie = 33

H1: At least one of these proportions is different from the distribution specified in H0.

H0: prestaurant = pgrocery = pmovie

H1: At least one of these proportions is different from the others

H0: prestaurant = 0.392, pgrocery = 0.284, pmovie = 0.324

H1: At least one of these proportions is different from the distribution specified in H0.

H0: prestaurant = 0.40, pgrocery = 0.29, pmovie = 0.33

H1: At least one of these proportions is different from the distribution specified in H0.

10. The 2014 Community College Survey of Student Engagement (CCSSE) included a question that asked faculty how much of their coursework emphasizes the memorization of facts, ideas, or methods so that students can repeat them in pretty much the same form. The results are below.

Very little: 21.5% Some: 33.7% Quite a bit: 27.7% Very much: 17.1%

A small study that same year asked 400 randomly selected community college students how much of their coursework emphasized memorizing facts, ideas, or methods so that they can repeat them in pretty much the same form. The results are below.

Very little: 39 Some: 139 Quite a bit: 148 Very much: 74

Identify the CONCLUSION of a hypothesis test of the claim that the distribution of faculty responses to this question is the same as the distribution of student responses. Use a significance level of 0.01.

There is sufficient evidence to warrant rejection of the claim.

There is not sufficient evidence to warrant rejection of the claim.

There is not sufficient evidence to support the claim.

There is sufficient evidence to support the claim.

12. The 2014 Community College Survey of Student Engagement (CCSSE) included a question that asked faculty how much of their coursework emphasizes the memorization of facts, ideas, or methods so that students can repeat them in pretty much the same form. The results are below.

Very little: 21.5% Some: 33.7% Quite a bit: 27.7% Very much: 17.1%

Very little: 39 Some: 139 Quite a bit: 148 Very much: 74

Find the value of the P-VALUE that would be used in a test of the claim that the distribution of faculty responses to this question is the same as the distribution of student responses. Use a significance level of 0.01.

approximately 0

1.94710-8 (or 0.000 000 019 47)

2.34710-14 (or 0.000 000 000 000 023 47)

approximately 1

13. Suppose that an observed frequency of 30 corresponds to an expected frequency of 27. Compute the contribution that this observed frequency makes towards the total value of the ? test statistic in a goodness-of-fit test or a test of independence.

0.1

0.111

0.333

0.3

14. The 2014 Community College Survey of Student Engagement (CCSSE) included a question that asked faculty how much of their coursework emphasizes the memorization of facts, ideas, or methods so that students can repeat them in pretty much the same form. The results are below.

Very little: 21.5% Some: 33.7% Quite a bit: 27.7% Very much: 17.1%

Very little: 39 Some: 139 Quite a bit: 148 Very much: 74

Find the absolute value of the CRITICAL VALUE that would be used in a test of the claim that the distribution of faculty responses to this question is the same as the distribution of student responses. Use a significance level of 0.01.

12.838

14.860

13.277

11.345

15. The 2014 Community College Survey of Student Engagement (CCSSE) included a question that asked faculty how much of their coursework emphasizes the memorization of facts, ideas, or methods so that students can repeat them in pretty much the same form. The results are below.

Very little: 21.5% Some: 33.7% Quite a bit: 27.7% Very much: 17.1%

Very little: 39 Some: 139 Quite a bit: 148 Very much: 74

Find the value of the TEST STATISTIC that would be used in a test of the claim that the distribution of faculty responses to this question is the same as the distribution of student responses. Use a significance level of 0.01.

38.765

-0.0977

66.542

3641.84

16. The 2014 Community College Survey of Student Engagement (CCSSE) included a question that asked faculty how much of their coursework emphasizes the memorization of facts, ideas, or methods so that students can repeat them in pretty much the same form. The results are below.

Very little: 21.5% Some: 33.7% Quite a bit: 27.7% Very much: 17.1%

Very little: 39 Some: 139 Quite a bit: 148 Very much: 74

What are the HYPOTHESES that would be used in a test of the claim that the distribution of faculty responses to this question is the same as the distribution of student responses?

H0: pvery little = 0.0975, psome = 0.3475, pquite a bit = 0.37, pvery much = 0.185

H1: at least one of these proportions is different from the distribution in H0

H0: pvery little = 39, psome = 139, pquite a bit = 148, pvery much = 74

H1: at least one of these proportions is different from the distribution in H0

H0: pvery little = 0.215, psome = 0.337, pquite a bit = 0.277, pvery much = 0.171

H1: at least one of these proportions is different from the distribution in H0

H0: pvery little = psome = pquite a bit= pvery much

H1: at least one of these proportions is different from the others

35. Assume that a random sample consisting of n = 46 pairs of data was collected. For a significance level of ? = 0.05, find the critical rs values that would be used in a rank correlation test using this sample data.

0.292

0.294

0.370

0.245

38. In a study of 25 smokers who tried to quit smoking with nicotine patch therapy, 14 were smoking one year after the treatment. Use the sign test with a 0.01 significance level to test the claim that among smokers who try to quit with nicotine patch therapy, the majority are smoking a year after the treatment.

Identify the CONCLUSION of a hypothesis test of the claim.

There is sufficient evidence to warrant rejection of the claim.

There is not sufficient evidence to warrant rejection of the claim.

There is not sufficient evidence to support the claim.

There is sufficient evidence to support the claim.

39. In a study of 25 smokers who tried to quit smoking with nicotine patch therapy, 14 were smoking one year after the treatment. Use the sign test with a 0.01 significance level to test the claim that among smokers who try to quit with nicotine patch therapy, the majority are smoking a year after the treatment.

Identify the value of the CRITICAL VALUE used in a hypothesis test of the claim.

-2.33

-2.575

41. In a study of 25 smokers who tried to quit smoking with nicotine patch therapy, 14 were smoking one year after the treatment. Use the sign test with a 0.01 significance level to test the claim that among smokers who try to quit with nicotine patch therapy, the majority are smoking a year after the treatment.

Identify the value of the TEST STATISTIC used in a hypothesis test of the claim.

-0.4

0.8

42. In a study of 25 smokers who tried to quit smoking with nicotine patch therapy, 14 were smoking one year after the treatment. Use the sign test with a 0.01 significance level to test the claim that among smokers who try to quit with nicotine patch therapy, the majority are smoking a year after the treatment.

Identify the correct HYPOTHESES used in a hypothesis test of the claim.

H0: p = 0.5

H1: p

H0: median = 0.5

H1: median

H0: median = 0.5

H1: median > 0.5

H0: p = 0.5

H1: p > 0.5

45. It is believed that in family physician practices the median amount of time that doctors and physician assistants spend with the patient per appointment is 20 minutes. However, it is claimed that the median amount of time spent with Medicaid patients is less than 20 minutes. A random sample of 12 appointments by Medicaid patients was selected, and the time that the doctor and physician assistants spent with them is recorded below. Test the claim at the 0.025 significance level.

15.6 20.2 18.1 19.5 23.5 20.4 16.2 12.4 9.6 23.8 18.4 14.7

Identify the value of the CRITICAL VALUE used in a hypothesis test of the claim.

-1.96

46. It is believed that in family physician practices the median amount of time that doctors and physician assistants spend with the patient per appointment is 20 minutes. However, it is claimed that the median amount of time spent with Medicaid patients is less than 20 minutes. A random sample of 12 appointments by Medicaid patients was selected, and the time that the doctor and physician assistants spent with them is recorded below. Test the claim at the 0.025 significance level.

15.6 20.2 18.1 19.5 23.5 20.4 16.2 12.4 9.6 23.8 18.4 14.7

Identify the value of the TEST STATISTIC used in a hypothesis test of the claim.

-0.866

1.443

47. It is believed that in family physician practices the median amount of time that doctors and physician assistants spend with the patient per appointment is 20 minutes. However, it is claimed that the median amount of time spent with Medicaid patients is less than 20 minutes. A random sample of 12 appointments by Medicaid patients was selected, and the time that the doctor and physician assistants spent with them is recorded below. Test the claim at the 0.025 significance level.

15.6 20.2 18.1 19.5 23.5 20.4 16.2 12.4 9.6 23.8 18.4 14.7

Identify the correct HYPOTHESES used in a hypothesis test of the claim.

H0: median = 20

H1: median ? 20

H0: median = 20

H1: median > 20

H0: median = 20

H1: median

48. For the following sequence of sample nominal data (with two categories), conduct a runs test for randomness, using ? = 0.05.

1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 0 1

Identify the DECISION and CONCLUSION of this runs test.

Reject H0.

The sequence appears to be random.

Fail to reject H0.

The sequence appears to be random.

Fail to reject H0.

The sequence does NOT appear to be random.

Reject H0.

The sequence does NOT appear to be random.

49. For the following sequence of sample nominal data (with two categories), conduct a runs test for randomness, using ? = 0.05.

P P Q Q P Q P P Q Q P Q P P

Identify the DECISION and CONCLUSION of this runs test.

Reject H0.

The sequence appears to be random.

Fail to reject H0.

The sequence appears to be random.

Fail to reject H0.

The sequence does NOT appear to be random.

Reject H0.

The sequence does NOT appear to be random.

50. For the following sequence of sample nominal data (with two categories), conduct a runs test for randomness, using ? = 0.05.

Y N Y N N Y N Y Y Y N Y N Y N Y Y Y N Y N Y N N Y Y Y Y N Y N Y N Y Y

Identify the value(s) of the CRITICAL VALUE(S) used in this runs test.

1.96

10 and 23

11 and 24

1.645

51. For the following sequence of sample nominal data (with two categories), conduct a runs test for randomness, using ? = 0.05.

Y N Y N N Y N Y Y Y N Y N Y N Y Y Y N Y N Y N N Y Y Y Y N Y N Y N Y Y

Identify the value of the TEST STATISTIC used in this runs test.

2.577

52. For the following sequence of sample nominal data (with two categories), conduct a runs test for randomness, using ? = 0.05.

1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 0 1

Identify the value(s) of the CRITICAL VALUE(S) used in this runs test.

9 and 21

5 and 14

1.96

53. For the following sequence of sample nominal data (with two categories), conduct a runs test for randomness, using ? = 0.05.

1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 0 1

Identify the value of the TEST STATISTIC used in this runs test.

-3.036

54. For the following sequence of sample nominal data (with two categories), conduct a runs test for randomness, using ? = 0.05.

P P Q Q P Q P P Q Q P Q P P

Identify the value(s) of the CRITICAL VALUE(S) used in this runs test.

6 and 16

3 and 12

1.96

55. For the following sequence of sample nominal data (with two categories), conduct a runs test for randomness, using ? = 0.05.

P P Q Q P Q P P Q Q P Q P P

Identify the value of the TEST STATISTIC used in this runs test.

0.650

56. For the following sequence of sample nominal data (with two categories), conduct a runs test for randomness, using ? = 0.05.

Y N Y N N Y N Y Y Y N Y N Y N Y Y Y N Y N Y N N Y Y Y Y N Y N Y N Y Y

Identify the DECISION and CONCLUSION of this runs test.

Reject H0. The sequence appears to be random.

Fail to reject H0. The sequence appears to be random.

Fail to reject H0. The sequence does NOT appear to be random.

Reject H0. The sequence does NOT appear to be random.

57. The state's Gaming Control Board does random inspections of casino games. An inspector observed 40 spins of the roulette wheel in a certain casino, and she recorded whether the result was a red number ("r") or a black number ("b"). (Assume that none of these results was a "0" or "00," which are green numbers.) Her observations are given below (the first row has the first 20 observations, and the second row has the next 20 observations). At the 0.05 significance level, test the claim that the red and black numbers occur in a random order.

b r r b b r b r b r b r r b r b b b b b

r r r r r r b r r r b r b r r r b r b b

Identify the value of the TEST STATISTIC used in the hypothesis test of this claim.

1.036

0.712

0.230

Consider the linear model Y = alX1 + a2X2 +b where the vector (X1, X2 ) has a bivariate Gaussian distribution with means U1, M2, variances of, 0?, and correlation coefficient p12. Consider the vector (X1, Y). One can show (via some involved calculus) that (X1, Y ) has a bivariate Gaussian distribution. Determine its two means, two variances, covariance, and correlation coefficient.\f3. Consider the model Yt = Bo+ BIXt + ut E(ujX) = 0 ut = put-1+ Et Ipl