Question

A major oil company has developed a new gasoline additive that is supposed to increase mileage. To test this hypothesis, ten cars are randomly selected. The cars are driven both with and without the additive. The results are displayed in the following table. Can it be concluded, from the data, that the gasoline additive does significantly increase mileage?

Let d=(gas mileage with additive)−(gas mileage without additive)d=(gas mileage with additive)−(gas mileage without additive). Use a significance level of α=0.05α=0.05 for the test. Assume that the gas mileages are normally distributed for the population of all cars both with and without the additive.

Car	1	2	3	4	5	6	7	8	9	10
Without additive	16.6	11	29.3	28.5	26.5	20.1	16	25.4	10.7	19.3
With additive	17.3	13.2	30	29.5	28.7	23.2	19.1	28.4	13.8	20.4

State the null and alternative hypotheses for the test

Find the values of the two sample proportions, pˆ1 and pˆ2. Round to 3 decimal places

Compute the weighted estimate of p, p‾. Round to 3 decimal places

Compute the value of the test statistic. Round to 2 decimal places

Determine the decision rule for rejecting the null hypothesis H_0. Round to 3 decimal places [ (Reject H₀ if (t or absolute value of t) is (< or >)   (value) ]

Make a decision to reject or fail to reject the null hypothesis.

Answer 1

Following table shows the calculations:

Without additive	With additive	d	(d-mean)^2
16.6	17.3	0.7	1.7424
11	13.2	2.2	0.0324
29.3	30	0.7	1.7424
28.5	29.5	1	1.0404
26.5	28.7	2.2	0.0324
20.1	23.2	3.1	1.1664
16	19.1	3.1	1.1664
25.4	28.4	3	0.9604
10.7	13.8	3.1	1.1664
19.3	20.4	1.1	0.8464
Total		20.2	9.896

Sample size: n =8

Now,

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