A publisher wants to estimate the mean sales per bookstore of a particular book.

Question

A publisher wants to estimate the mean sales per bookstore of a particular book. Suppose a simple random sample of 100 bookstores selected from a population of 1000 bookstores results in 20 of them being Small in size, 30 being Medium, and 50 being Large. Furthermore, suppose three independent simple random subsamples of 2, 3, and 5 bookstores are selected from the 20 Small, 30 Medium, and 50 Large bookstores, respectively. The numbers of copies of the particular book sold by these 10 bookstores are as follows: What special kind of sampling is being employed in this survey? Briefly describe its major components.

Explanation / Answer

(a) This is an example of stratified sampling, where the poulation is divided into groups based on their size and then obtain a simple random sample from each group (stratum) and collect data on each sampling unit that was randomly sampled from each group (stratum).

Here, a sample of 100 bookstores was taken in which 20 of them are small in size, 30 in medium and 50 are big in size. Small, medium and big size are different stratas of the population (bookstore). Then smple random samples were collected from each group (stratum).

(b) mean number of books sold in small bookstore = (34+26)/2 = 30

mean number of books sold in medium bookstore = (120+66+84)/3 = 90

mean number of books sold in large bookstore = (322+281+198+325+174)/5 = 260

mean number of books sold in sampled 100 bookstores = (20*30 + 30*90 + 50*260)/100 = 163

Standard deviation for the given data of 10 bookstores = 115.32

Standard error = 115.32/sqrt(10) = 36.46

For 95 % confidence interval, z-value is 1.96, so the bound on the error of the estimation

= 1.96 * 36.46 = 71.46

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