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 98 adults 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%).

1. What will the hypotheses be?

H_o:

H_a:

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

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

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

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

Answer 1

Solution :

Given that,

= 17.6 miles

s = 7.8 miles

n = 98

a.) Hypothesis:

H0 :    16 miles

Ha : > 16 miles

Test Statistic:

t = ( - ) / (s /n)

t = (17.6 - 16 ) / ( 7.8/ 98)

t = 2.031

P - value = 0.0225

if P- value < 0.05 then reject H0.

P-value = 0.0225 < 0.05, we reject H0.

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