Problem 2. (7 points)

In a test involving highway cruising at 70 miles per hour, nine new cars of a certain make were randomly selected from the production line. Each car was driven 200 miles without an oil additive and 200 miles with an oil additive. Let X₁ and X₂ denote the miles per gallon for a car with and without the oil additive, respectively. Data on the observed miles per gallon is summarized below.

	MPG with Additive (X1)	MPG without Additive (X2)
1	32.02	30.13
2	26.19	21.42
3	28.03	27.08
4	26.77	25.94
5	27.71	29.09
6	33.77	32.28
7	28.79	27.77
8	31.84	30.35
9	28.64	25.59

Test the research hypothesis that the mean difference,m_d, in the observed miles per gallon for a car with and without the oil additive is greater than zero (i.e., the additive leads to an increase in miles per gallon on average). Give the null and alternative hypotheses, compute the test statistic and p-value. What do you conclude? Usea = 0.05.