Question

assume a significance level of \\( \alpha=0.05 \\) and use the given information to complete parts (a) and (b) below. original claim: less than \\( 49 \\% \\) of adults would erase all of their personal information online if they could. the hypothesis test results in a p-value of 0.047. a. state a conclusion about the null hypothesis. (reject \\( h_{0} \\) or fail to reject \\( h_{0} \\).) choose the correct answer below. a. fail to reject \\( h_{0} \\) because the p-value is less than or equal to \\( \alpha \\). b. fail to reject \\( h_{0} \\) because the p-value is greater than \\( \alpha \\). c. reject \\( h_{0} \\) because the p-value is greater than \\( \alpha \\). d. reject \\( h_{0} \\) because the p-value is less than or equal to \\( \alpha \\). b. without using technical terms, state a final conclusion that addresses the original claim. which of the following is the correct conclusion? a. the percentage of adults that would erase all of their personal information online if they could is less than \\( 49 \\% \\). b. there is not sufficient evidence to support the claim that the percentage of adults that would erase all of their personal information online if they could is less than \\( 49 \\% \\). c. there is sufficient evidence to support the claim that the percentage of adults that would erase all of their personal information online if they could is less than \\( 49 \\% \\). d. the percentage of adults that would erase all of their personal information online if they could is more than or equal to \\( 49 \\% \\).

Explanation:

Step1: Recall the decision rule for hypothesis testing

In hypothesis testing, if the \(P - value\leq\alpha\), we reject the null hypothesis \(H_0\). Here, \(\alpha = 0.05\) and \(P - value=0.047\). Since \(0.047<0.05\) (i.e., \(P - value\leq\alpha\)).

Step2: Analyze part (a)

For part (a), because \(P - value = 0.047\leq\alpha=0.05\), we reject \(H_0\).

Step3: Analyze part (b)

When we reject the null hypothesis, it means there is sufficient evidence to support the alternative hypothesis. The original claim is the alternative hypothesis (less than \(40\%\)).

Answer:

a. D. Reject \(H_0\) because the \(P -\)value is less than or equal to \(\alpha\).
b. C. There is sufficient evidence to support the claim that the percentage of adults that would erase all of their personal information online if they could is less than \(40\%\).