Sovi.AI - AI Math Tutor

Scan to solve math questions

QUESTION IMAGE

assume a significance level of \\( \\alpha = 0.1 \\) and use the given …

Question

assume a significance level of \\( \alpha = 0.1 \\) 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 0.0073. a. state a conclusion about the null hypothesis. (reject \\( h _ { 0 } \\) or fail to reject \\( h _ { 0 } \\).) choose the correct answer below. \\( \bigcirc \\) a. fail to reject \\( h _ { 0 } \\) because the p - value is less than or equal to \\( \alpha \\). \\( \bigcirc \\) b. reject \\( h _ { 0 } \\) because the p - value is greater than \\( \alpha \\). \\( \bigcirc \\) c. fail to reject \\( h _ { 0 } \\) because the p - value is greater than \\( \alpha \\). \\( \bigcirc \\) d. 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 the null hypothesis \(H_0\). If \(P - value>\alpha\), we fail to reject the null hypothesis \(H_0\). Here, \(\alpha = 0.1\) and \(P - value=0.0073\).

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

Since \(0.0073<0.1\) (i.e., \(P - value\leq\alpha\))

Answer:

D. Reject \(H_0\) because the P - value is less than or equal to \(\alpha\)