Chapter 5.1, Problem 5.10E

(a)

To determine

To explain why this sampling method gives each member of the faculty an equal chance to be chosen.

Explanation of Solution

  $100$ of the $1000$ men are randomly selected, thus any man has one chance in ten of being selected.

  $\frac{100}{1000}=\frac{1}{10}$

  $50$ of the $500$ females are randomly selected, thus any women has one chance in ten of being selected.

  $\frac{50}{500}=\frac{1}{10}$

We then note that men and women are equally likely to be selected and each individual has one chance in ten of being selected.

(b)

To determine

To explain why this is not SRS.

Explanation of Solution

A simple random sample(SRS) is a sample in which each possible sample has an equal chance of being selected.

The sample is, in this case, not a simple random sample(SRS), because a sample of only men is not possible to select, while a sample of $100$ men and $50$ women is possible to select.