The problem is to estimate the sales for the coming year for a maker of industrial equipment.

Question:

The problem is to estimate the sales for the coming year for a maker of industrial equipment. The forecast is based on asking customers how much they are planning to order next year. To use the research budget efficiently, the customers are stratified by the size of their orders during the past year. The following is some relevant information based on the past year:

a. Assume that a total of 300 interviews are to be conducted. How would you allocate those interviews among the three strata?
b. If a simple random sample of size 300 were obtained from the population, about 10 percent, or 30 interviews, would be from the large-customer stratum. Why did you recommend in part (a) that more than 30 interviews be conducted from this stratum?
c. The survey was conducted, and the average values (in thousands) for each stratum were as follows:
1 = 100
2 = 8
3 = 5
What would your estimate be of the population mean, the average sales that will be received from all customers next year?
d. Given the context of part (c), what would be the variance of your estimate of the population mean? Do you think that this variance would be larger or smaller than the variance of your estimate of the population mean if you had taken a simple random sample of size 300 from the total population? Why?
e. What is the total interviewing cost, given a cost per interview of $64, and 300 interviews?
f. Assume now that it has been decided that the small customers can be contacted by telephone, making their cost per interview only $9 each. Repeat the analysis that you did for part (a). How would you allocate 300 interviews now?
g. Now, under part (f), what is the total interviewing cost?
h. How many interviews could you conduct, assuming that you had the same amount of money determined under part (e), that you allocated the interviews according to your answer in part (f), and that the costs were as in part (f)?