Problem

Assume a significance level of $\alpha=0.05$ and use the given information to complete parts (a) and (b) below. Original claim: More than $51 \%$ of adults would erase all of their personal information online if they could. The hypothesis test results in a P-value of 0.0185. 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. Reject $\mathrm{H}_{0}$ because the P-value is greater than $\alpha$. B. Reject $\mathrm{H}_{0}$ because the P-value is less than or equal to $\alpha$. C. Fail to reject $H_{0}$ because the P-value is less than or equal to $\alpha$. D. Fail to reject $\mathrm{H}_{0}$ because the P-value is greater than $\alpha$.

Solution

Step 1 :The null hypothesis, denoted by H0, is a statement of no effect or no difference and is assumed to be true until we have enough evidence to decide otherwise. The alternative hypothesis, denoted by H1, is a statement that indicates the presence of an effect or a difference. In this case, the null hypothesis would be that 51% or less of adults would erase all of their personal information online if they could, and the alternative hypothesis would be that more than 51% of adults would do so.

Step 2 :The P-value is a measure of the probability that we would observe the data we have, or data more extreme, if the null hypothesis were true. If the P-value is less than or equal to the significance level (α), we reject the null hypothesis in favor of the alternative hypothesis. If the P-value is greater than α, we do not have enough evidence to reject the null hypothesis.

Step 3 :In this case, the P-value is 0.0185 and the significance level is 0.05. Therefore, the P-value is less than the significance level.

Step 4 :Final Answer: \(\boxed{\text{B. Reject } H_{0} \text{ because the P-value is less than or equal to } \alpha}\)

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Source: https://solvelyapp.com/problems/22751/

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