Question

In a recent publication, it was reported that the average highway gas mileage of tested models of a new car was 33.5 mpg. A consumer group conducts its own tests on a simple random sample of 12 cars of this model and finds that the mean gas mileage for their vehicles is 31.6 mpg with a standard deviation of 3.4 mpg.

a) Choose an appropriate significance test for the consumer group to perform to test the publication's assertion.

b) The conditions to use the test are not met. What condition fails?

c) Proceed with the test you chose anyway. Test whether or not the true gas mileage of this model car is less than the published value.

d) If you were to test whether the car has an average mileage that is different than the publication stated, what would your results show?

e) Why is there a difference between the answers to c) and d)?

Answer 1

a) Choose an appropriate significance test for the consumer group to perform to test the publication's assertion.

One-Sample t-test

b) The conditions to use the test are not met. What condition fails?

Normal distribution

c) Proceed with the test you chose anyway. Test whether or not the true gas mileage of this model car is less than the published value.

The hypothesis being tested is:

H0: µ = 33.5

Ha: µ < 33.5

33.500	hypothesized value
31.600	mean 1
3.400	std. dev.
0.981	std. error
12	n
11	df
-1.936	t
.0395	p-value (one-tailed, lower)

The p-value is 0.0395.

Since the p-value (0.0395) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the true gas mileage of this model car is less than the published value.

d) If you were to test whether the car has an average mileage that is different than the publication stated, what would your results show?

The hypothesis being tested is:

H0: µ = 33.5

Ha: µ ≠ 33.5

33.500	hypothesized value
31.600	mean 1
3.400	std. dev.
0.981	std. error
12	n
11	df
-1.936	t
.0790	p-value (two-tailed)

The p-value is 0.0790.

Since the p-value (0.0790) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that µ ≠ 33.5.

e) Why is there a difference between the answers to c) and d)?

Becuase the research hypothesis is different.