Question

assume a significance level of $\alpha = 0.01$ and use the given information to complete parts (a) and (b) below. original claim: the mean pulse rate (in beats per minute) of a certain group of adult males is 73 bpm. the hypothesis test results in a p - value of 0.0765. a. state a conclusion about the null hypothesis (reject $h_0$ or fail to reject $h_0$). choose the correct answer below. a. fail to reject $h_0$ because the p - value is greater than $\alpha$. b. fail to reject $h_0$ because the p - value is less than or equal to $\alpha$. c. reject $h_0$ because the p - value is less than or equal to $\alpha$. d. reject $h_0$ because the p - value is greater than $\alpha$. b. without using technical terms, state a final conclusion that addresses the original claim. which of the following is the correct conclusion? a. there is not sufficient evidence to warrant rejection of the claim that the mean pulse rate (in beats per minute) of the group of adult males is 73 bpm. b. there is sufficient evidence to warrant rejection of the claim that the mean pulse rate (in beats per minute) of the group of adult males is 73 bpm. c. the mean pulse rate (in beats per minute) of the group of adult males is 73 bpm. d. the mean pulse rate (in beats per minute) of the group of adult males is not 73 bpm.

Explanation:

Step1: Compare P - value and significance level

We are given \(\alpha = 0.01\) and \(P - value=0.0765\). Since \(0.0765>0.01\) (i.e., \(P - value>\alpha\)).

Step2: Make decision about null hypothesis

When \(P - value>\alpha\), we fail to reject the null hypothesis \(H_0\).

Step3: Relate to original claim

Since we fail to reject the null hypothesis (which is the claim in this case, because the original claim is about the mean being a specific value and in hypothesis testing for a mean \(\mu\), \(H_0:\mu = 73\)), we say there is not sufficient evidence to reject the claim.

Answer:

a. A. Fail to reject \(H_0\) because the P - value is greater than \(\alpha\)
b. A. There is not sufficient evidence to warrant rejection of the claim that the mean pulse rate (in beats per minute) of the group of adult males is 73 bpm.