Youâll find data on the time required to perform a repetitive task (in seconds) on an assembly line for two workers. Farnsworth has been doing this task for months, whereas Higgenbottom just started. A sample of 70 times is provided in the worksheet. (adapted from [Albright et al. 2011]) a. Find a 95% confidence interval for the mean time it takes Farnsworth to perform the task. Do the same for Higgenbottom.

b. Do you believe both of the confidence intervals in part a are valid and/or useful? Why or why not? As a decision maker, whose mean time would you rather have and why?

Use the same date set. The times are shown in chronological order.

c. Find a 95% confidence interval for the standard deviation of times for Farnsworth. Do the same for Higgenbottom. What do these confidence intervals indicate?

d. Given that these times are listed chronologically, how useful are the confidence intervals in part c? Specifically, is there any evidence that the variation in times is changing through time for either of the two workers?


166.475.6
263.875.1
369.374.6
464.276.1
555.771.6
672.573.7
766.275.8
864.081.8
968.373.3
1066.173
1164.377.8
1267.174.8
1370.161.3
1465.769.7
1563.068.7
1659.076.1
1759.177.7
1865.971
1967.871.6
2077.062.3
2165.466.4
2270.578.3
2365.270.9
2473.370
2563.270.9
2665.670
2763.266.5
2862.771.9
2961.167.8
3065.270.1
3164.672.1
3270.070.7
3365.860.3
3468.265.7
3570.268.6
3668.870.4
3758.561.4
3863.862.7
3964.064
4068.569.5
4169.062.3
4256.866.1
4364.862.1
4460.168
4566.860.6
4673.064.7
4766.060.6
4862.562.3
4969.759.1
5065.860.8
5165.268
5269.661.6
5364.858.3
5470.555.8
5561.367.8
5665.864.1
5767.963.9
5868.860.2
5964.162.3
6060.561.1
6163.663.4
6267.664.5
6366.458.5
6464.160.1
6572.162.9
6666.657.2
6766.063.5
6871.965.7
6965.664.7
7058.857.4