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  3. a manager wishes to see if the time (in minutes) i

A manager wishes to see if the time (in minutes) it takes for their workers to...

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Question

Statistics

A manager wishes to see if the time (in minutes) it takes fortheir workers to complete a certain task is different if they arewearing earbuds.   A random sample of 20 workers' timeswere collected before and after wearing earbuds. Test the claimthat the time to complete the task will be different, i.e. meaninghas production differed at all, at a significance level of α =0.01

For the context of this problem, μD =μbefore−μafter where the first data setrepresents before earbuds and the second data set represents theafter earbuds. Assume the population is normally distributed. Thehypotheses are:

H0: μD = 0
H1: μD  0

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

59.8

35.5

73.1

77

49.9

38.4

56.2

55.4

64.3

55.6

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