Question

1. Suppose it is claimed that the typical adult travels an average distance of 16 miles to get to work each day. You believe this average is too low for Columbus residents. You survey a random sample of 98adults from Columbus and find that your sample travels an average distance of 17.6 miles to work each day, with a sample standard deviation of 7.8 miles.   Use this information to conduct the appropriate hypothesis test by going through the steps you learned about from our Chapter 22 and Chapter 23 lecture videos (and from your reading of Chapters 22 and 23). Assume the alpha level is .05 (or 5%).

A. What will the hypotheses be?

Ho:

Ha:

B. Use the following formula to compute the test statistic.

C. Based on what you see in Table B, what should the p-value be?

D. Will you reject or fail to reject the null hypothesis? Please state your decision and the reason why you are making that decision.

E. In general, if we end up rejecting the null hypothesis when conducting a hypothesis test, we say our results are _________________________ significant.

Answer 1

The provided sample mean is 17.6 and the sample standard deviation is s = 7.8, and the sample size is n = 98

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho:  μ = 16

Ha: μ > 16

This corresponds to a right-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, and the critical value for a right-tailed test is t_c = 1.661

(3) Test Statistics

The t-statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that t = 2.031> t_c = 1.661, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p = 0.0225, and since p = 0.0225 < 0.05, it is concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean μ is greater than 16, at the 0.05 significance level.

A. What will the hypotheses be?

Ho: = 16

Ha: > 16

B. Use the following formula to compute the test statistic.

2.031

C. Based on what you see in Table B, what should the p-value be?

0.0225

D. Will you reject or fail to reject the null hypothesis? Please state your decision and the reason why you are making that decision.

Reject the null hypothesis

E. In general, if we end up rejecting the null hypothesis when conducting a hypothesis test, we say our results are statistically significant.