Sampling Theory

1. A certain manufacturing firm produces a product that is packaged under two brandnames for marketing purposes. These two brands serve as strata for estimating potential sales volume for the next quarter. A simple random sample of customers for each brand is contacted and asked to provide a potential sales figure? (in number of units) for the coming quarter. Last year’s true sales figure for the same quarter, is available for each of the sampled customers and is denoted by x. The data are given in the accompanying table. The sample for Brand I was taken from a list of 120 customers for whom the total sales in the same quarter of last year was 24,500 units. The Brand I1 sample came from 180 customers with a total quarterly sales last year of 21,200 units.

Brand I      Brand II

• Compute the combined ratio estimate of the total potential sale in the next quarter and place a bound on the error of estimation. (10 marks)

1

• Estimate the total sale in the next quarter under stratified random sampling and place a bound on the error of estimation. (10 marks)
• Compare the precision of the estimates in parts (a) and (b) above and give

reason(s) for what you observe.                                                                   (3 marks)

2. Show that the sample size for estimating a population mean with an error bound B

using cluster sampling is  where.