A car manufacturer wants to compare the performance of engines using ethanol mix with that of those using pure gasoline. They start by randomly choosing 200 cars, and divide that sample into two equally sized groups. The sample average performance for 100 cars using ethanol is 76.5 on a 0 to 100 scale, and the sample standard deviation is 38. For the other sample of cars, they test using pure gasoline and the average performance is 88.1 and the sample standard deviation is 40. 1

• Build a 95% confidence interval for the performance score of the ethanol cars. Can we reject a null hypothesis that their true score is 39 at the 5% significance level?
• Now we will compare them directly to the non-ethanol cars. Test the null hypothesis that the two groups have the same average score, assuming they have the same variance.
• Now perform the same test assuming they have differing variances. How do the results differ?
• (Extra Credit) Suppose you tried to answer this question using regression analysis. Define which dependent and independent variable you would use, and say what your slope and intercept estimates would be (reporting actual numbers, not formulas).