Problem

Assume a significance level of $\alpha=0.05$ and use the given information to complete parts (a) and (b) below.
Original claim: Less than $46 \%$ of adults would erase all of their personal information online if they could. The hypothesis test results in a P-value of 0.0319 .
a. State a conclusion about the null hypothesis. (Reject $\mathrm{H}_{0}$ or fail to reject $\mathrm{H}_{0}$.) Choose the correct answer below.
A. Fail to reject $\mathrm{H}_{0}$ because the P-value is less than or equal to $\alpha$.
B. Reject $\mathrm{H}_{0}$ because the P-value is greater than $\alpha$.
C. Reject $\mathrm{H}_{0}$ because the P-value is less than or equal to $\alpha$.
D. Fail to reject $\mathrm{H}_{0}$ because the $\mathrm{P}$-value is greater than $\boldsymbol{\alpha}$.

Answer

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Answer

\(\boxed{\text{Therefore, we reject } H_0 \text{ because the P-value is less than or equal to } \alpha.}\)

Steps

Step 1 :Given that the significance level (\(\alpha\)) is 0.05 and the P-value is 0.0319.

Step 2 :The null hypothesis (\(H_0\)) is that the proportion of adults who would erase all of their personal information online if they could is equal to or greater than 46%.

Step 3 :The alternative hypothesis is the original claim that less than 46% of adults would do so.

Step 4 :The P-value is the probability of obtaining a result as extreme as, or more extreme than, the observed result, under the assumption that the null hypothesis is true.

Step 5 :If the P-value is less than or equal to the significance level, we reject the null hypothesis. If the P-value is greater than the significance level, we fail to reject the null hypothesis.

Step 6 :In this case, the P-value (0.0319) is less than the significance level (0.05).

Step 7 :\(\boxed{\text{Therefore, we reject } H_0 \text{ because the P-value is less than or equal to } \alpha.}\)

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