Question

Simple Random Sample Which of the following is are simple random samples?

a. As Lipitor pills are being manufactured, a quality control plan is to select every 500th pill and test it to confirm that it contains 80 mg of atorvastatin.

b. To test for a gender difference in the way that men and women make online purchases, Gallup surveys 500 randomly selected men and 500 randomly selected women.

c. A list of all 10,877 adults in Trinity County, California, is obtained; the list is numbered from 1 to 10,877; and then a computer is used to randomly generate 250 different numbers between 1 and 10,877. The sample consists of the adults corresponding to the selected numbers.

Short answer

c. is a simple random sample.

Step-by-step solution

Step 1:Simple random sample

A simple random sample is considered a mode of data collection where each observation is randomly chosen from one population (providing an equal chance of selection to each item).

Explanation for the sampling method

a.

Given: Each of the 500^th Lipitor pill is selected to test that the amount of atorvastatin.

The sampling process does not provide an even chance of selection for each pill in the process. Only the first selection is random, and the subsequent ones are made in a specific pattern, that is, selecting the 500^th pill.

Thus, the sampling is not a simple random sampling but a systematic sampling.

Explanation for the sampling method

b.

Given: Each of the 500 randomly selected men and women is evaluated to check the gender difference in the online purchases.

The samples are collected from two different groups of men and women. The chances of selection for men and women from the population of people who made online purchases are not even as the numbers of men and women differ in population.

Thus, the sampling method is not simple random sampling.

Explanation for the sampling method

c.

Given: The sampling process followed is:

• List all adults from 1 to 10877, in count.
• Select the adults corresponding to 250 randomly generated numbers from 1 to 10877.

In this case, each of the 10877 adults has an even chance to be selected in the sample of 250 as the draws are clearly random and computer generated.

Thus, the sampling method is simple random sampling.