Question

Many drivers of cars that can run on regular gas actually buy premium in the belief that they will get better gas mileage. To determine if there is evidence to support this claim, 10 cars were used in a company fleet in which all of the cars ran on regular gas. Each car was filled first with either regular or premium gasoline, decided by a coin toss, and the mileage was recorded for a tank full. Then, the mileage was recorded again for the same cars for a tank full of the other kind of gasoline. The results are listed below in miles per gallon: Car # 1 2 3 4 5 6 7 8 9 10 Regular 16 20 21 22 23 22 27 25 27 28 Premium 19 20 24 19 25 25 26 26 28 28

The test of the variances at .10 reveals that we reject the null hypothesis. Yes or no

There is a statistically significant difference between the mean of regular gas and the mean of premium gas as evidenced by the respective sample means. Yes or no

The standard error of the mean difference is 1.969 Yes or no'

For the test of the means at .05, we fail to reject the null hypothesis. Yes or no

For the test of the means at .05, the decision is reject the null hypothesis. yes or no

For the test of the means at .05, the final conclusion within the context of the scenario is that there is sufficient evidence to indicate that regular and premium get about the same gas mileage. Yes or no

For the 2-tail test of the confidence interval, the confidence interval contains 0 . Yes or no

For the 2-tail test of the confidence interval, the decision is to fail to reject the null b/c 0 is not in the interval. Yes or no

For the 2-tail test of the confidence interval, the evidence is because 0 is in the interval. Yes or no

Because we failed to reject the null hypothesis, this indicates that there is no difference in gas mileage between premium and regular. Yes or no

Answer 1

a)

Here paired t test will be used. Let d = premium - regular

Hypotheses are:

Following table shows the calculations;

Premimum	Regular	d	(d-mean)^2
19	16	3	4.41
20	20	0	0.81
24	21	3	4.41
19	22	-3	15.21
25	23	2	1.21
25	22	3	4.41
26	27	-1	3.61
26	25	1	0.01
28	27	1	0.01
28	28	0	0.81
Total		9	34.9

sample size: n =10

Now

The standard error of mean difference is

So test statistics will be

P-value of the test for t=1.45 and df=n-1=10-1=9 will be 0.1823.

Since p-value is greater than 0.05 so we fail to reject the null hypothesis.

For the test of the means at .05, the final conclusion within the context of the scenario is that there is sufficient evidence to indicate that regular and premium get about the same gas mileage. Yes

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For 90% confidence interval t critical value for df=9 is 1.833. So required confidence interval will be

So required confidence interval is (-0.242, 2.042).

Because we failed to reject the null hypothesis, this indicates that there is no difference in gas mileage between premium and regular. Yes