Question

A simple random sample of 31 men from a normally distributed population results in a standard deviation of 7.2 beats per minute. The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal? range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.05 significance level to test the claim that pulse rates of men have a standard deviation equal to ? beats per minute.

Identify the null and alternative hypotheses.

Compute the test statistic

Find the p-value

Answer 1

a) As we are trying to test the claim here that the standard deviation of the pulse rate distribution is equal to 10, therefore the null and alternate hypothesis here are given as:

b) Now we are given the sample standard deviation here as s = 7.2 with sample size n = 31

The test statistic here is computed as:

Therefore 15.552 is the test statistic value required here.

c) Now as this is a two tailed test, the p-value for n - 1 = 30 degrees of freedom is computed from the chi square distribution tables as:

Therefore 0.0276 is the required p-value here.