Suppose that in question 61 we are interested in knowing how large a sample to take for:

(a) A proportional allocation.

(b) An optimal allocation, assuming the stratum population standard deviations are the same as the corresponding sample values.

Question 61

A movie theater chain has 35 theaters in California, 50 in New York, and 45 in Pennsylvania. Management is considering adding a new snack item to its concession stands. In order to determine whether this new snack will be a success, management tested the product in 10 theaters in California, 12 in New York, and 9 in Pennsylvania for 1 month. The sample means and standard deviations for the numbers of purchases are shown here.

(a) Use an unbiased estimation procedure to find an estimate of the mean number of purchases per movie theater in a month for all 130 movie theaters.

(b) Find an estimate of the variance of the estimator in part (a), using an unbiased estimation procedure.

(c) Find a 90 % confidence interval for the population mean number of purchases per theater.

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Mean Standard deviation California 100.4 40.3 New York 98.2 21.7 Pennsylvania 77.6 45.1