Step 1 :The null hypothesis in this case is that the standard deviation of pulse rates of a certain group of adult males is not more than 14 bpm. The alternative hypothesis is that the standard deviation is more than 14 bpm.
Step 2 :The P-value is the probability of obtaining a result as extreme as, or more extreme than, the observed data, assuming that the null hypothesis is true. If the P-value is less than or equal to the significance level, we reject the null hypothesis. If the P-value is greater than the significance level, we fail to reject the null hypothesis.
Step 3 :In this case, the P-value is 0.2952 and the significance level is 0.05. Therefore, we fail to reject the null hypothesis because the P-value is greater than the significance level. So, the correct answer for part a is C. Fail to reject \(H_{0}\) because the \(P\)-value is greater than \(\alpha\).
Step 4 :Since we fail to reject the null hypothesis, this means that there is not sufficient evidence to support the claim that the standard deviation of pulse rates of the group of adult males is more than 14 bpm. So, the correct answer for part b is C. There is not sufficient evidence to support the claim that the standard deviation of pulse rates of the group of adult males is more than 14 bpm.
Step 5 :\(\boxed{\text{For part a, the correct answer is C. Fail to reject } H_{0} \text{ because the } P \text{-value is greater than } \alpha.}\)
Step 6 :\(\boxed{\text{For part b, the correct answer is C. There is not sufficient evidence to support the claim that the standard deviation of pulse rates of the group of adult males is more than 14 bpm.}}\)