For one of the tasks in a manufacturing process, the mean time for task completion has historically


Question: For one of the tasks in a manufacturing process, the mean time for task completion has historically been 35.0 minutes, with a standard deviation of 2.5 minutes. Workers have recently complained that the machinery used in the task is wearing out and slowing down. In response to the complaints, plant engineers have measured the time required for a sample consisting of 100 minutes (below). Using the mean for this sample, and assuming that the population standard deviation has remained unchanged at 2.5 minutes, construct the 95% confidence interval for the population mean. Is 35.0 minutes within the confidence interval? Interpret your yes or no answer in terms of whether the mean time for the task may have changed.


Minutes
41.7
35.54
35.31
35.04
40.61
33.25
39.36
34.88
37.89
38.3
37.86
33.7
35.68
32.64
38.72
32.99
34.08
36.57
32.24
34.65
32.43
34.44
37.03
34.62
34.97
41.63
37.67
38.51
39.26
39.14
34.2
37.28
36.35
36.11
39.16
38.72
37.33
40.89
37.35
38.96
36.55
31.82
37.69
36.85
40.73
37.72
37.67
37.32
38.6
40.47
35.15
37.75
36.51
39.13
33.3
35.33
41.05
29.04
37.21
39.76
34.47
43.76
39.54
33.41
34.82
34.97
38.98
35.68
38.53
35.21
36.09
36.38
34.92
38.01
41.71
32.31
37.21
36.17
37.8
35.3
37
35.51
40.27
38.6
38.01
36.68
37.92
30.71
35.08
35.84
34.89
37.1
38.57
41.41
38.9
37.35
37.33
34.39
33.84
35.77

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