Question

Testing Normality For the hypothesis test describ\({n_2} = 153\)ed in Exercise 2, the sample sizes are\({n_1} = 147\)and. When using the Ftest with these data, is it correct to reason that there is no need to check for normality because \({n_1} > 30\)and\({n_2} > 30\)?

Short answer

Although the samples have more than 30 values, the Ftestrequires that the samples must be strictly normally distributed regardless of how large the samples are.

Thus, the given reason is incorrect.

Step-by-step solution

Given information

A sample of size 147 is considered showing the heights of women. Another sample of size 153 is considered showing the heights of men.

Normality requirement of F test

To perform the F test, it is a strict requirement that the populations from which the two samples are taken should be normally distributed, irrespective of their sample sizes.

Here, it is mentioned that the sample sizes of the two samples are large (147 and 153). Hence, there is no need to check for the normality of the populations.

This reason is incorrect because the F test will not result in an accurate conclusion if the samples are not from normally distributed populations.

Thus, it is important to check the normality using normal quantile plots. One cannot rely on the samples being large in order to perform the F test.