Question

A simple random sample of 44 men from a normally distributed population results in a standard deviation of 8.6 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 10 beats per minute. Complete parts? (a) through? (d) below.

Answer 1

Here, we are testing whether the standard deviation is equal to 10 beats per minute. Therefore the null and the alternative hypothesis here are given as:

The test statistic here is computed as:

Now for n - 1 = 43 degrees of freedom, we get from the chi square distribution tables that:

As the p-value here is 0.2084 > 0.05 which is the level of significance, therefore the test is not significant and we cannot reject the null hypothesis here. Therefore, we dont have sufficient evidence here to reject the claim that the standard deviation is 10 beats per minute.