Question

According to the U.S. Federal Highway Adminisdatiol, the men number of miles driven annually in 2008 was 10,300. You believe that people are driving more today than in 2008. A simple random sample of 20 drivers yields an average of 11,400 highway miles driven last year. Assuming s-4.300, test your hypothesis at the α-10 level. a. What are the null and alternative hypotheses? b. What is the specific name of the hypotheses test you will carry out? c. What is the P-value from your test? d. State your conclusion (reject the null or fail to reject the null) in coherent and well-written sentences within the context of this situation. e. Are your results statistically significant? Explain why or why not in coberent, well-written sentences. f. What type of error might you have made and what are the consequences of such an error?

Answer 1

Solution:

Null hypothesis H0: mean <=10300

Alternate hypothesis H1: mean >10300

As our sample size is less than 30 and population standard deviation is unknown we will use student t test.

Test statistic =(11400-10300)/4300/sqrt(20)

Test statistic = (1100/4300/4.4721) = 1.1440

So this is right tailed test and df=19

So p-value from t table is 0.133

Alpha value =0.1

As we can see that our p-value is greater than alpha value so we are failed to reject null hypothesis.

So we can not support the claim that people are driving more than 10300

Our result is not significant as p-value is greater than alpha value(0.133>0.1) so our result is not significant.