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SCM 200 – Exam 3 – Practice Exam Solutions

1. A – The p-value of 0.16 says there is a 0.16 probability of getting a value greater than 50. That means that there must be a 0.84 probability of getting a value less than 0.15 (1 – 0.16 = 0.84).

2. A – Reject the claim by accepting Ho.

n = 100 p = 22 / 100 = 0.22 α = 0.01

Ho: π = 0.15 Ha: π > 0.15 (claim)

z =𝑝 − 𝜋

√𝜋(1 − 𝜋)𝑛

=0.22 − 0.15

√0.15(1 − 0.15)100

= 1.96

p-value = 0.025 α = 0.01 p-value > α = Accept null, reject alternative hypothesis (Apple’s claim)

3. C – Paired sample t-test for mean differences.

4. C – Ha: μD > 0. The problem tells you that the difference is (Old – New). The

chef wants to see if the new time is faster. If the new time is faster, the difference will be a positive number.

5. C – 8.18

t =D̅ − μD

SD

√n

=1.8 − 0

1.1

√25

= 8.18

6. E – Both C and D. If Ho is rejected at a 1% level of significance, it will be rejected at higher levels of significance as well.

7. C – 75% of the variation in y can be explained by x.

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8. E – Gym time, speed, and max bench press. You are looking for variables that have a p-value greater than 0.01.

9. A – (0.195, 0.405)

n = 100 p = 30 / 100 = 0.30

Value to look up in z-table = (1 – 0.9786) / 2 = 0.0107 z-score = 2.30

Confidence interval = p ± z√𝑝(1 − 𝑝)

𝑛

0.30 ± 2.30√0.30(1 − 0.30)

100= 0.30 ± 0.1054 = (0.195, 0.405)

10. C – Conclude claim is not true by rejecting Ho

n =36 μD = 11 D̅ = 13 SD = 4 α = 0.05 df = 35

Ho: μD ≤ 11 (claim) Ha: μD > 11

t =D̅ − μD

SD

√n

=13 − 11

4

√36

= 3.00

0.005 < p-value < 0.001

11. D – The standard error of the estimate keeps the original data units of y.

12. C – 113

df = (50 + 65) – 2 = 113

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13. B – 0.167

p̂ =(x1 + x2)

(n1 + n2)=

100 + 150

500 + 1,000= 0.167

14. B – 61% of the variation in college GPA can be explained by SAT score.

15. A – You use the coefficient of determination to find the value of the

correlation coefficient. You know the sign on the correlation coefficient is negative because the regression equation has a negative slope.

R2 = 0.64 r = √0.64 = 0.8

16. B – 16%

r = 0.40 R2 = 0.16

17. D – Slope of the regression line.

18. C – Use the coefficient column in the Excel output to determine the multiple

regression equation.

19. D – 676

π = 0.50 E = 0.05

z-value in table = (1 – 0.9906) / 2 = 0.0047 z-score = 2.60

n = π(1 − π) [𝑧

𝐸]

2

= 0.50(1 − 0.50) [2.60

0.05]

2

= 676

20. B – Less than 20%

Ho: π ≥ 0.20 Ha: π < 0.20

21. B – 29

df = 30 – 1 = 29

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22. B – You know the value of the correlation coefficient was calculated incorrectly because the value of the correlation coefficient must be between –1 and 1.

23. A – t = 0.949

𝑠p = √(𝑛1 − 1)𝑠1

2 + (𝑛2 − 1)𝑠22

𝑛1 + 𝑛2 − 2

𝑠p = √(14 − 1)62 + (11 − 1)42

14 + 11 − 2= √

628

23= 5.23

t =(�̅�1 − �̅�2) − (𝜇1 − 𝜇2)

𝑠𝑝√1𝑛1

+1

𝑛2

t =(14 − 12) − (0)

5.23√ 114 +

111

= 0.949

24. C – 0.80 < p-value < 0.90

t = 0.949 df = (14 + 11) – 2 = 23

25. B – The researcher can conclude a linear relationship exists between the

variables because the p-value of 0.045 is less than the significance level of 0.05.

26. C – Paired sample t-test for mean difference because each package is shipped from the same location using both UPS and FedEx.

27. B – Ha: μD ≠ 0 because the problem says Amazon wants to test if UPS has

different shipping times than FedEx.

28. A – Negative 2.00

t =D̅ − μD

SD

√n

=−1 − 0

3.5

√49

= −2

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29. A – 0

30. C – Wider than the confidence interval for the mean.

31. D – Seasonality

32. D – Correlation coefficient

33. D – Conclude that the true slope for the population is equal to zero because the p-value of 0.088 is greater than the level of significance. This means that we cannot reject the null hypothesis. The null hypothesis in a simple linear regression is that the true slope for the population is equal to zero.

34. B – Higher, Lower

35. D – Greater than 30%

Ho: π ≤ 0.30 Ha: π > 0.30

36. A – Random variation

37. A – Smaller than

Confidence interval for the mean value of y for a given level of x – Calculated using the following equation

�̂� ± 𝐭𝐒𝐞

√𝐧

Prediction interval for a particular value (the next value) of y for a given level of x – Calculated using the following equation

�̂� ± 𝐭𝐒𝐞

38. B – The coefficient of determination is equal to one

39. B – Dummy variables

40. B – Correlation coefficient

41. True

42. False – Slope is not the same thing as the correlation coefficient. Slope is an example of a regression coefficient.

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43. True

44. True

45. True

46. True – Make sure to double the value found using the t-table because the problem says that it is a two-tailed test.

47. True

48. False – Each units ads $1,750 to the total cost.

49. False – The coefficient of determination is always positive, between 0 and 1.

The correlation coefficient tells you about the slope of the regression equation because its value can be either positive or negative.

50. True

51. True

52. True

53. False – Slope can be positive or negative.

54. False – These terms are not interchangeable.

55. True

56. False – R Square adjusted will usually be less than the unadjusted R Square.

57. False

b1 = rSy

Sx= 0.88 (

3.95

5.50) = 0.63

58. False

p-value = 0.035 Alpha = 0.01 Accept Ho; there is no linear relationship because the p-value is greater than the alpha.

59. True

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60. True – The independent variable (X) will be time and the dependent variable (Y) will be sales.

61. False – The coefficient of determination (R2) can take any value between 0

and 1. The correlation coefficient (r) can take any value between –1 and 1.

62. False – The coefficient of determination (R2) does indicate the strength of the relationship between the independent and dependent variable; however, it does not show whether the relationship is positive or negative.

63. False – The response variable is the y-variable. There is only one y-variable

in a multiple linear regression. There are multiple x-variables.

64. False – It is possible for the y-intercept to be positive or negative.

65. True

66. False – The sign of the correlation coefficient tells us the sign of the slope so the values must always have the same sign.

67. False

df = 4 – 1 = 3 t = 2.353 Lookup t = 2.353 with df = 3 in table = 0.950 However, this is the p-value for a less than test and we are doing a ≠ test. ≠ p-value = 2(1 – 0.950) = 0.10

68. False – The regression coefficients, b0 and b1, can both have values less than

negative 1.

69. False – The strongest correlation is the correlation with an absolute value closest to 1.

70. True

71. True

72. True

73. True

74. False – Correlation does not prove causation.

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75. True

76. True – The predictor variables are the X variables in multiple linear regressions; however, there is only one Y variable in multiple linear regressions.

77. True

P(Z > 1.30) = 1 – 0.9032 = 0.0968