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. b. without using technical terms, state a final conclusion that addresses the original claim. which of the following is the correct conclusion? \\( \bigcirc \\) a. 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 more than 58%. \\( \bigcirc \\) b. the percentage of adults that would erase all of their personal information online if they could is less than or equal to 58%. \\( \bigcirc \\) c. the percentage of adults that would erase all of their personal information online if they could is more than 58%. \\( \bigcirc \\) d. 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 more than 58%.

Explanation:

When the P - value ($0.0284$) is less than the significance level ($\alpha = 0.05$), we reject the null hypothesis. In non - technical terms, a small P - value means the result is unlikely to occur by chance if the null hypothesis were true. Since the original claim is that more than 58% of adults would erase their personal information (this is the alternative hypothesis in a hypothesis test), and we reject the null hypothesis (which would be the opposite of the claim, i.e., $p\leq0.58$), it means there is evidence for the claim.

Answer:

D. 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 more than 58%.