Question

The fuel economy sticker on a new SUV’s window sticker indicates the owner can expect 16 mpg in city driving and 20 mpg highway driving and 18 mpg overall. Accurate gasoline records for one such vehicle were kept, and a random sample of mileage per tank of gasoline was collected:

17.6	17.7	18.1	22.0	17.0	19.4	18.9	17.4	21.0	19.2
18.3	19.1	20.7	16.7	19.4	18.2	18.4	17.1	17.4	15.8
17.9	18.0	16.3	17.5	17.3	20.4	19.1	21.0	18.1	19.0
19.6	18.9	16.8	18.2	17.6	19.1	18.0	16.8	20.9	17.9
17.7	20.3	18.6	19.0	16.5	19.4	18.6	18.6	17.3	18.7

Test whether the population average mpg is actually greater than 18 mpg using a 1% level of significance.

1. State the null and alternate hypotheses.
   
2. Would you perform a one-tailed or two-tailed test? Why?
   
3. State the test statistic and p-value of your test. Round your values to four-decimal places.
   
4. Explain your conclusion to reject or fail to reject the null hypothesis in terms of p and α.
   
5. Interpret your conclusion in the context of this problem.
   
6. Explain if your conclusion agrees with the confidence interval you calculated for this information in question 4.

Answer 1

Solution

The provided sample mean is X = 18.45 and the sample standard deviation is s = 1.344, and the sample size is n = 50. (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: 4 = 18 Ha: u > 18 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 a = 0.01, and the critical value for a right-tailed test is te = 2.405. The rejection region for this right-tailed test is R=t:t > 2.405 (3) Test Statistics The t-statistic is computed as follows: X po t= = 18.45 – 18 1.344/50 = 2.368 8/ Vn

(4) Decision about the null hypothesis Since it is observed that t = 2.368 <tc = 2.405, it is then concluded that the null hypothesis is not rejected. Using the P-value approach: The p-value is p= 0.0109, and since p=0.0109 > 0.01, it is concluded that the null hypothesis is not rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population average mpg is actually greater than 18 mpg using a 1% level of significance.

Since confidence interval includes 18 so null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population average mpg is actually greater than 18 mpg using a 1% level of significance.

Confidence Interval The 99% confidence interval is 17.941 <u<18.959.