Q 23. Is it an SRS? A corporation empl... [FREE SOLUTION]

91影视

The Practice of Statistics for AP

David Moore,Daren Starnes,Dan Yates

$Math Studyset 91影视 Explanations$ Math

4th Edition 路 809 pages

ISBN: 9781319113339

Chapter 4: Q 23. (page 228)

Is it an SRS? A corporation employs $2000$ male and $500$ female engineers. A stratified random sample of $200$ male and $50$ female engineers gives each engineer $1$ chance in $10$ to be chosen. This sample design gives every individual in the population the same chance to be chosen for the sample. Is it an SRS? Explain your answer.

Short Answer

Expert verified

We are only interested in $200$ male and $50$ female engineers, some samples of size $250$ are less likely to be selected. There is no chance of a sample of $250$ females or $250$ males being selected.

Step by step solution

Given information

No. of male engineers = $2000$

No. of female engineers $= 500$

Sample size of male engineers $= 200$

Sample size of female engineers $= 50$

Concept

A simple random sample (SRS) of size n is made up of $n$ people chosen from the population with an equal chance of being the sample that is actually chosen.

Explanation

Every person in the population has the same chance as the selected sample of $200$ male and $50$ female engineers. An SRS ensures that any sample of a given size has the same chance of being chosen. It is not an SRS since the selected sample of $200$ male and $50$ female engineers offers each individual in the population the same chance, but it does not give every conceivable sample of $250$ engineers the same chance. Because we are only interested in $200$ male and $50$ female engineers, some samples of size $250$ have a lower chance of being chosen. A sample of $250$ females or $250$ males has no chance of being chosen.