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: The standard deviation of pulse rates of adult males is more than 11 bpm. The hypothesis test results in a P-value of 0.3045.

Short answer

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

b. There is not sufficient evidence to conclude that the standard deviation of the pulse rate of adult males is more than 11 bpm.

Step-by-step solution

Given information

A claim is tested that the standard deviation of pulse rates of adult males is more than 11 bpm.

The p-value for this test is equal to 0.3045.

Hypotheses

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

Null Hypothesis: The standard deviation of the pulse rate of adult males is equal to 11 bpm.

Alternative Hypothesis: The standard deviation of the pulse rate of adult males is more than 11 bpm.

In terms of notation, the null and alternative hypotheses can be written as:

$$\begin{gathered} H_0:\sigma =11 \\ {H}_1:\sigma >11 \end{gathered}$$

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 0.3045.

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

Conclusion

b.

There is not sufficient evidence to support the claim that the standard deviation of the pulse rate of adult males is more than 11 bpm.