Question

assume a significance level of \\( \alpha = 0.05 \\) and use the given information to complete parts (a) and (b) below. original claim: more than 58% of adults would erase all of their personal information online if they could. the hypothesis test results in a p - value of 0.0284. 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 less than or equal to \\( \alpha \\). b. reject \\( h _ { 0 } \\) because the p - value is greater than \\( \alpha \\). c. fail to 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 greater than \\( \alpha \\).

Explanation:

The decision rule for hypothesis testing using the P - value method is: 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, \(\alpha = 0.05\) and \(P - value=0.0284\). Since \(0.0284<0.05\) (i.e., \(P - value\leq\alpha\)).

Answer:

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