one
The Small Business Administration (SBA) wishes to estimate the mean annual sales of companies that employ fewer than 20 persons. Historical data suggest that the standard deviation of annual sales of such companies is about $5500 (a) If the SB A wants to estimate mean annual sales to within $1000 with a probability of 0.90, how large a sample should be chosen? (b) Suppose that the SBA has a tolerable type I error rate of 10%. It wishes to detect a difference in mean annual sales of $500 with a probability of 0.95. How large a sample should be chosen?
two
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 other
Losses, what premium should the company charge to make an average net profit of 1.5% of the policy’s face value?
