Part 1 of 5 An automotive maker researcher wants to compare the effect of two fuel additives on the average gas mileage of the new car model. The fuel consumption {in miles per gallon) was recorded for 22 cars running for 1 week using the first additive, and then the average miles per gallon were recorded for 19 cars running for 1 week using the second additive. Fuel additive 1 : 44.7 44.7 43.9 44.8 51.6 47.3 48.9 46.7 43.3 45.9 42.9 44.3 41.8 42.9 44.7 42.7 46.5 44.6 44 45.7 (Note: The average and the standard deviation of the data are respectively 44.8 mpg and 2.4 mpg.) Fuel additive 2: 37.5 49.1 41.8 38.3 49.7 39.2 40.6 41.6 38.8 46.7 44.1 43.3 38.5 33.4 44.5 37.8 42.3 44 37.5 (Note: The average and the standard deviation of the data are respectively 41.5 mpg and 4.23 mpg.) Use 10% level of significance to decide whether there is sufficient evidence that the average gas mileage from using the first fuel additive is greater than the average gas mileage from using the second fuel additive. You may also assume that the samples are from normal populations. Hint: The standard deviation for the rst sample appears to be different from the standard deviation of the second sample. To check this claim the two-tail F-test for two variances can be set up which will result in the p-value of 0.014. Use the significance level of 10% to interpret this as sufficient or insufficient evidence that the two populations have different standard deviations and then decide whether to use the pooled or non-pooled procedure. Procedure: I Select an answer v | Assumptions: (select everything that applies} I] Normal populations I] Population standard deviations are known [:1 Paired samples El Simple random samples C] Independent samples III Population standard deviation are unknown but assumed equal III Sample sizes are both greater than 30 C] Population standard deviation are unknown and not assumed equal I] The number of positive and negative responses are both greater than 10 for both samples