A simple random sample of 32 men from a normally distributed population results in a standard deviation of 8.8 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 0.10 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.
a. Identify the null and alternative hypotheses. Choose the correct answer below.
A. $\mathrm{H}_{0}: \sigma=10$ beats per minute $H_{1}: \sigma \neq 10$ beats per minute
C. $\mathrm{H}_{0}: \sigma=10$ beats per minute $H_{1}: \sigma< 10$ beats per minute
b. Compute the test statistic.
\[
\chi^{2}=\square
\]
(Round to three decimal places as needed.)
B. $\mathrm{H}_{0}: \sigma \geq 10$ beats per minute $\mathrm{H}_{1}: \sigma< 10$ beats per minute
D. $\mathrm{H}_{0}: \sigma \neq 10$ beats per minute $H_{1}: \sigma=10$ beats per minute

Step 1 ：Identify the null and alternative hypotheses. The null hypothesis is that the standard deviation is equal to a specific value, and the alternative hypothesis is that the standard deviation is not equal to that value. The null and alternative hypotheses for this problem are: \(H_{0}: \sigma=10\) beats per minute, \(H_{1}: \sigma \neq 10\) beats per minute.

Step 2 ：Calculate the test statistic using the formula for the chi-square statistic: \(\chi^{2} = (n - 1) * (s^{2} / \sigma^{2})\), where n is the sample size, s is the sample standard deviation, and \(\sigma\) is the hypothesized population standard deviation. In this case, n = 32, s = 8.8, and \(\sigma\) = 10. The calculated chi-square statistic is approximately \(\boxed{24.006}\).

Step 3 ：Compare the calculated chi-square statistic to the critical value for the chi-square distribution with n - 1 degrees of freedom to determine whether to reject the null hypothesis. The significance level for this test is 0.10. The critical value of the chi-square distribution with 31 degrees of freedom at the 0.10 significance level is approximately \(\boxed{44.985}\).

Step 4 ：Since the calculated chi-square statistic (24.006) is less than the critical value (44.985), we do not reject the null hypothesis. Therefore, there is not enough evidence at the 0.10 significance level to support the claim that the standard deviation of pulse rates of men is not equal to 10 beats per minute.