Suppose that in question 64, a sample of 35 restaurants is to be taken. Determine how the sample should be allocated among the three states for

(a) A proportional allocation.

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

Question 64

A fast-food chain has 25 restaurants in Alabama (Ala.), 20 in Louisiana (La.), 25 in Texas (Tex.), and 32 in Arkansas (Ark.). Management is considering adding a hamburger item to its menu. In order to determine whether this burger will be a success, management tested the product in 15 restaurants in Alabama, 11 in Louisiana, 18 in Texas, and 5 in Arkansas for 1 week. The sample means and standard deviations for the numbers of purchases are shown here.

where X̅ and s are the mean and standard deviation, respectively.

(a) Use an unbiased estimation procedure to find an estimate of the mean number of purchases of the burgers for all 102 restaurants

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

(c) Find a 99 % confidence interval for the population mean number of burgers sold per restaurant.

Transcribed Image Text:

S Ala. 127.5 83.3 La. 221.3 43.8 Tex. 99.7 27.6 Ark. 127.6 70.2