# Use standard deviation of sample or population in z test

I am reading the book Statistics by Witte & Witte. Some questions puzzle me.

Question 10.9:

The normal range for a widely accepted measure of body size, the body mass index (BMI), ranges from 18.5 to 25. Using the midrange BMI score of 21.75 as the null hypothesized value for the population mean, test this hypothesis at the .01 level of significance given a random sample of 30 weight-watcher participants who show a mean BMI = 22.2 and a standard deviation of 3.1.

The chapter explains the z test. It uses the following formula.

z = (mean_sam - mean_pop) / (stdev_pop / sqrt(n))


In the question only a standard deviation of the sample is given. I don't no whether and how this affects this formula.

## 1 Answer

There are different tests (z/Gauss-test and t-test) depending on whether the population stdev is known or the sample stdev is plugged in.

• thank you Then I conclude the question is misguiding. – pikachu May 30 '20 at 11:45
• Actually for large samples the two are pretty much the same (equivalent for $n \to\infty$), and even for $n=30$ they shouldn't give you something too different. – Lewian May 30 '20 at 13:28