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The personnel manager wants to determine if there is a difference in the average time lost due to absenteeism between two plants. From historical data, the estimated standard deviations of lost time are 200 and 250 minutes, respectively, for plants 1 and 2.

(a) Assuming that equal sample sizes will be selected from each plant, what should the sample size be if the bound on the error of estimation is 40 minutes with a probability of 0.90?

(b) If the unit sampling costs are less in plant 1 compared to plant 2 such that a sample that is twice as large could be selected from plant 1, what are the respective sample sizes?

(c) Suppose that it is desired to detect a difference of 30 minutes in the lost time with a probability of 0.80. Assume that there is no significant difference in the standard deviations of lost time. For a chosen level of significance of 0.10, what should the sample size be assuming samples of equal size from both plants?

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