Solutions Statistics

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

Question: For one of the tasks in a manufacturing process, the mean tine 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 100 tasks operations. The 100 sample times, in minutes, are in data file XR09022. Using the mean of the 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” answers in terms of whether the mean time for the task may have change.

(File XR09022)

minutes
41.70
35.54
35.31
35.04
40.61
33.25
39.36
34.88
37.89
38.30
37.86
33.70
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
34.20
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
38.60
40.47
35.15
37.75
36.51
39.13
33.30
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
37.80
35.30
37.00
35.51
40.27
38.60
38.01
36.68
37.92
30.71
35.08
35.84
34.89
37.10
38.57
41.41
38.90
37.35
37.33
34.39
33.84
35.77