Page | 2 1. The manufacturer of a gasoline additive dalins that the use of this additive Increases gasoline mileage. A random sample of 6 cars was selected, and these cars were driven for one week without the gasoline additive and then for one week with the additive. The following table gives the mileage (in miles per gallon) for these carswith and without the additive: Car 3 5 6 Mileage Without Additive 24.6 28 5 189 23.7 15.4 29.5 Mileage With Additive 26.3 31.7 18 2 25.3 18.3 30.5 (a) Construct a 90% confidence Interval for the mean difference In gas mileage (with - without). [4 pts] (b) Assuming mileages are normally distributed, test the manufacturer's claim at the 2.5% significance level. 1. Define the parameter(s) and state the hypotheses: [2pts] li. Find the observed sample statistic (using your calculator) and the test statistic (using a formula). Use proper notation for the sample statistic ( x or p ), and clearly identify your test statistic as either a z-score or a t-score. [3pt]