Question

Final Conclusions. In Exercises 25–28, use a significance level of = 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.

Short answer

a. The null hypothesis fails to reject at a 0.05 level of significance.

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

Step-by-step solution

Given information

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.

Identify the hypotheses

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

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

Null Hypothesis : p = 0.58

Alternative Hypothesis : $p>0.58$

Decision about the test

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.

Conclusion

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.