Question

assume a significance level of α = 0.05 and use the given information to complete parts (a) and (b) below. original claim: more than 47% of adults would erase all of their personal information online if they could. the hypothesis test results in a p - value of 0.2544. 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 α. b. fail to reject ( h_0 ) because the p - value is less than or equal to α. c. fail to reject ( h_0 ) because the p - value is greater than α. d. reject ( h_0 ) because the p - value is less than or equal to α.

Explanation:

Step1: Recall the decision rule for hypothesis testing

If \(P - value\leq\alpha\), reject \(H_0\). If \(P - value>\alpha\), fail to reject \(H_0\).

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

Given \(\alpha = 0.05\) and \(P - value=0.2544\). Since \(0.2544>0.05\) (i.e., \(P - value>\alpha\)).

Answer:

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