A marathon was conducted in large city on September 3 1989 B

A marathon was conducted in large city on September 3, 1989. Based on the entry applications, the following data were obtained. It is desired to take a sample of approximately 500 persons front this list for purposes of estimating the average number of miles run per week in preparation for this marathon. If it is assumed that this might be proportional to the number of marathons completed. is there much to be gained by using a stratified random sample with proportional allocation over simple random sample?

Solution

Here using a stratified random sampling with proprtional allocation will be more helpful than simple random sample.Now allocation of random sampling is done when one needs to allocate a total sample size n among some identified strata. Now, if the strata differs in size then allocation of sample sizes to strata must be proprtional to stratum sizes. So, stratified random sampling with proprtional allocation should be used here.