Question

assume a significance level of \\( \alpha = 0.05 \\) and use the given information to complete parts (a) and (b) below. original claim: the standard deviation of pulse rates of a certain group of adult males is more than 12 bpm. the hypothesis test results in a p - value of 0.2211. a. state a conclusion about the null hypothesis. (reject \\( h _ { 0 } \\) or fail to reject \\( h _ { 0 } \\).) choose the correct answer below. ○ a. reject \\( h _ { 0 } \\) because the p - value is greater than \\( \alpha \\). ○ b. fail to reject \\( h _ { 0 } \\) because the p - value is greater than \\( \alpha \\). ○ c. reject \\( h _ { 0 } \\) because the p - value is less than or equal to \\( \alpha \\). ○ d. fail to reject \\( h _ { 0 } \\) because the p - value is less than or equal to \\( \alpha \\).

Explanation:

Step1: Recall the decision rule for hypothesis testing

If \(P - value\leq\alpha\), we reject \(H_0\). If \(P - value>\alpha\), we fail to reject \(H_0\). Here, \(\alpha = 0.05\) and \(P - value=0.2211\).

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

Since \(0.2211>0.05\) (i.e., \(P - value>\alpha\))

Answer:

B. Fail to reject \(H_0\) because the P - value is greater than \(\alpha\).