25 suppose that 10,000 customers in a retailer's customer database are categorized by three customer types: 3,500 prospective buyers, 4,500 first time buyers, and 2,000 repeat (loyal) buyers. a sample of 1,000 customers is needed. what type of sampling should you do? why? explain how you would carry out the sampling according to the method stated in (a). why is the sampling in (a) not simple random sampling?

a. The object of every sampling exercise is to obtain a sample that truly represents the population. Since the retail customer's database has three classes or strata, we can use stratified sampling to obtain a sample.

b. We need to choose a sample of 1000 customers from the data.

We can find the proportion of each strata to the entire population and choose those many customers from each strata for the sample. The total number of customers in the database is 10,000. The proportion of prospective buyers to the total is 35% (3500/10000). So, 35% or 350 (1000 * 0.35) the observations in the sample will come from the prospective buyers' strata. Similarly, the sample will have 450 observations from the first buyers' strata, while 200 observation will come from the repeat buyers' strata. Once the number of observations for each strata is fixed, we can randomly select the desired number from each strata.

c. In simple random sampling, we don't classify the data into different groups based on different characteristics; we just randomly select a sample of 1000 from a population of 10,000.