Question

Requirements A researcher collects a simple random sample of grade-point averages of statistics students, and she calculates the mean of this sample. Under what conditions can that sample mean be treated as a value from a population having a normal distribution?

Short answer

If one of the following conditions is met, then the sample mean can be considered to come from a normally distributed population:

• It should be clearly stated that the sample from which the sample is extracted is normally distributed.

• The sample should have more than 30 observations.

Step-by-step solution

Given information

A simple random sample of grade-point averages of statistics students is considered.

The mean of this sample is calculated.

Requirements under which sample mean is considered to follow the normal distribution

One of the following requirements must be fulfilled for the computed sample mean to be treated as a value from a normally distributed population\.

• It should be mentioned that the population ofgrade-point averages of statistics students from which the sample is selected, isnormally distributed.

• The sample size should be greater than 30.