MATH 302 Quiz 2| Latest Solutions

Question 1                                                                                                                              1 / 1 point

A manager wishes to see if the time (in minutes) it takes for their workers to complete a certain task is different if they are wearing earbuds. A random sample of 20 workers' times were collected before and after wearing earbuds. Test the claim that the time to complete the task will be different, i.e. meaning has production differed at all, at a significance level of α = 0.01

For the context of this problem, μ_D = μ_before−μ_after where the first data set represents before earbuds and the second data set represents the after earbuds. Assume the population is normally distributed. The hypotheses are:

H₀: μ_D = 0 H₁: μ_D  0

You obtain the following sample data:

Before

After

69

65.3

69.5

61.6

39.3

21.4

66.7

60.4

38.3

46.9

85.9

76.6

70.3

77.1

59.8

51.3

72.1

69

79

83

61.7

58.8

55.9

44.7

56.8

50.6

71

63.4

80.6

68.9

Before

After

59.8

35.5

73.1

77

49.9

38.4

56.2

55.4

64.3

55.6

Find the p-value. Round answer to 4 decimal places. p-value:

___.0038___

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Question 2                                                                                                                          1 / 1 point

A manager wants to see if it worth going back for a MBA degree. They randomly sample 18 managers' salaries before and after undertaking a MBA degree and record their salaries in thousands of dollars. Assume Salaries are normally distributed. Test the claim that the MBA degree, on average, increases a manager's salary. Use a 10% level of significance.

t-Test: Paired Two Sample for Means

New Salary

Old Salary

Mean

61.878

56.999

Variance

177.5551

115.8012

Observations

18

18

Pearson Correlation

0.7464

Hypothesized Mean Difference

0

df

17

t Stat

2.9870

P(T<=t) one-tail

0.0024

t Critical one-tail

1.3334

P(T<=t) two-tail

0.0048

t Critical two-tail

1.7396

The hypotheses for this problem are: H₀: μ_D = 0

H₁: μ_D > 0

What is the correct test statistic? 2.9870

0.7464

1.7396

1.3334