Question

Is this an SRS? A large national telecommunications company has about 20,000 non-management employees and 3,000 management employees. A survey of employee opinion about recent changes in health care coverage selects 400 of the non-management employees at random and 60 of the management employees at random. The 460 employees make up the sample. a) Does this sampling method give each employee an equal chance to be chosen? Why or why not? b) Is this an SRS? Why or why not?

Answer 1

(a)

There are 20000 non-management employees and 400 were selected.

So, probability of a non-management employee to be selected = 400/20000 = 1/50

There are 3000 non-management employees and 60 were selected.

So, probability of a non-management employee to be selected = 60/3000 = 1/50

Clearly, the method gives each employee an equal chance to be chosen.

(b)

We know, SRS stands for Simple Random Sampling. While we use this sampling procedure, we choose sample from the whole population data set in each draw (with or without replacement).

So, this is not SRS.

This sampling procedure observed here is Stratified Random Sampling. In stratified random sampling, we divide the whole population into homogeneous strata of similar kind and then perform Simple Random Sampling (with or without replacement) in each strata to get sample and finally add all samples from all strata to get sample set.

Here also, whole population was divided into two homogeneous strata as management and non-management employees and simple random samples were drawn from both strata to obtain sample and finally all selected employees make up the sample.