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?

An insurance company wants to estimate the premium to be charged for a \$200,000
homeowner’s policy that covers fire, theft, vandalism, and natural calamities. Flood
and earthquakes are not covered. The company has estimated from historical data
that a total loss may happen with a probability of 0.0005, a 50% loss with a
probability of 0.001, and a 25% loss with a probability of 0.01. Ignoring all otherlosses, what premium should the company charge to make an average net profit of
1.5% of the policy’s face value?