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 $48%$ of adults would erase all of their personal information online if they could. the hypothesis test results in a $p - value$ of $0.2506$.
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 less than or equal to $alpha$
○ d. reject $h_0$ because the $p - value$ is greater than $alpha$
b. without using technical terms, state a final conclusion that addresses the original claim. which of the following is the correct conclusion?
○ 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 $48%$
○ b. the percentage of adults that would erase all of their personal information online if they could is more than $48%$
○ 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 more than $48%$
○ d. the percentage of adults that would erase all of their personal information online if they could is less than or equal to $48%$

Explanation:

Step1: Compare P - value and significance level

We are given that the significance level \(\alpha = 0.05\) and the P - value \(=0.2506\).
Since \(0.2506>0.05\) (i.e., \(P - value>\alpha\)).

Step2: Make a decision about the null hypothesis

The rule is: If \(P - value\leq\alpha\), we reject \(H_0\); if \(P - value>\alpha\), we fail to reject \(H_0\).
Because \(P - value = 0.2506>\alpha=0.05\), we fail to reject \(H_0\).

Step3: Relate the decision about \(H_0\) to the original claim

The original claim is \(p > 0.48\) (where \(p\) is the proportion of adults who would erase all of their personal information online if they could). The null hypothesis is \(H_0:p\leq0.48\).
Failing to reject \(H_0\) means that there is not enough evidence to support the claim that \(p > 0.48\).

Answer:

a. B. Fail to reject \(H_0\) because the \(P -\)value is greater than \(\alpha\)
b. 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 \(48\%\)