Final Conclusions. In Exercises 25–28, use a significance level of \(\alpha \) = 0.05 and use the given information for the following:

a. State a conclusion about the null hypothesis. (Reject \({H_0}\) or fail to reject \({H_0}\).)

b. Without using technical terms or symbols, state a final conclusion that addresses the original claim.

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 0.3257.

A claim is tested that more than 58% of adults would erase all of their personal information online if they could. The p-value for this test is equal to 0.3257.

The significance level is 0.05.

Let p be the population proportion of adults whowould erase all of their personal information online if they could.

In correspondence with the given claim, the following hypotheses are set up:

Null Hypothesis \[\left( {{H_0}} \right)\]: p = 0.58

Alternative Hypothesis\[\left( {{H_1}} \right)\]: \[p > 0.58\]

a.

If the p-value is less than the level of significance, the null hypothesis is rejected; otherwise, not.

Here, the level of significance is equal to 0.05, and the p-value is equal to 0.3257.

Since the p-value is greater than 0.05, so the decision fails to reject the null hypothesis.

b.

There is not sufficient evidence to support the claim that more than 58% of adults who would erase all of their personal information online if they could.