To compare two programs for training industrial workers to perform a skilled job, 20 workers are included in an experiment. Of these, 10 are selected at random and trained by method 1; the remaining 10 workers are trained by method 2. After completion of training, all the workers are subjected to a time-and-motion test that records the speed of per formance of a skilled job. The following data are obtained.

(a) Can you conclude from the data that the mean job time is significantly less after training with method 1 than after training with method 2? (Test with α = .05.)
(b) State the assumptions you make for the population distributions.
(c) Construct a 95% confidence interval for the population mean difference in job times between the two methods.

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Time (minutes) Method 1 15 20 11 23 16 21 18 16 27 24 Method 2 23 31 13 19 23 17 28 26 25 28