Question

a physical therapist wanted to know whether the mean step pulse of men was less than the mean step pulse of women she randomly selected 55 men and 79 women to participate in the study each subject was required to step up and down a 6 - inch platform the pulse of each subject was then recorded the following results were obtained (b) identify the p - value and state the researchers conclusion if the level of significance was \\( \alpha = 0.02 \\) what is the p - value? p - value \\( = 0.0052 \\) state the researchers conclusion. which of the following is correct? a. reject \\( h _ { 0 } \\), there is not sufficient evidence to conclude that the mean step pulse of men was less than the mean step pulse of women b. fail to reject \\( h _ { 0 } \\), there is sufficient evidence to conclude that the mean step pulse of men was less than the mean step pulse of women c. fail to reject \\( h _ { 0 } \\), there is not sufficient evidence to conclude that the mean step pulse of men was less than the mean step pulse of women d. reject \\( h _ { 0 } \\), there is sufficient evidence to conclude that the mean step pulse of men was less than the mean step pulse of women

Explanation:

Step1: Recall the decision rule for hypothesis testing

If \(P - value<\alpha\), we reject the null hypothesis \(H_0\). If \(P - value\geq\alpha\), we fail to reject the null hypothesis \(H_0\). Here, the null hypothesis \(H_0:\mu_{Men}=\mu_{Women}\) and the alternative hypothesis \(H_1:\mu_{Men}<\mu_{Women}\) (since we want to check if mean step - pulse of men is less than that of women). The significance level \(\alpha = 0.02\) and \(P - value=0.0052\).

Step2: Compare the P - value and \(\alpha\)

Since \(0.0052<0.02\) (i.e., \(P - value<\alpha\)).

Answer:

D. Reject \(H_0\), there is sufficient evidence to conclude that the mean step pulse of men was less than the mean step pulse of women