Question

a hotel rewards club wants to randomly select 100 of its 5,000 members to participate in a survey. the club wants to determine if peoples opinions differ based on age. there are 2,200 members between the ages of 25 and 50, and there are 2,800 who are age 51 or older. the club decides to randomly select 44 members between the ages of 25 and 50, and 56 members ages 51 and older. is the sample of 100 members a simple random sample?
yes, because the hotel rewards members were randomly selected for the sample.
yes, because each hotel rewards member has the same chance of being selected.
no, because the sample of 100 is too small a sample to represent the population.
no, because each sample of 100 does not have the same chance of being selected.

Explanation:

A simple random sample requires that every possible sample of the given size has an equal chance of being selected. In this case, the hotel rewards club divided the population into two age - based groups and selected a specific number from each group. This is stratified sampling, not simple random sampling. For example, a sample that had more members from the 25 - 50 age group (say 60 members) and fewer from the 51+ age group (40 members) could not be formed in this sampling method, which means not all samples of size 100 have the same chance of being selected.

Answer:

No, because each sample of 100 does not have the same chance of being selected.