Question

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: Fewer than 90% of adults have a cell phone. The hypothesis test results in a P-value of 0.0003.

Short answer

a.The null hypothesis is rejected at a 0.05 level of significance.

b. There is sufficient evidence to conclude that the percentage of adults who have cell phones is less than 90%.

Step-by-step solution

Given information

A claim is tested that less than 90% of adults have cell phones.

The p-value for this test is equal to 0.0003.

Hypotheses

Let p be the population proportion of adults who have cell phones.

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

Null Hypothesis\[\left( {{H_0}} \right):p = 0.90\]

Alternative Hypothesis \[\left( {{H_1}} \right):p < 0.90\]

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 0.0003.

Since the p-value is less than 0.05, the null hypothesis is rejected.

Conclusion of the test

b.

There is sufficient evidence to support the claim that the percentage of adults who have cell phones is less than 90%.