This assignment will get you to think a bit about how different tests involving two groups are different and can yield different results if we are not careful about which one, we choose to use. You will use the following dataset measuring the wear for two types of tires to answer the questions below: Automobile Wear on Tire Type A Wear on Tire Type B 10.6 10.2 9.8 9.4 12.3 118 9.7 9.1 8.8 8.3 Sample mean = 10.24 Sample mean = 9.78 Summary values Sample SD = 1.316 Sample SD = 1.328 Question 1: First let's assume that these are independent groups of automobiles (i.e. 5 cars use Type A tires and 5 cars use Type B) and that the population variances are equal. a) (3 points) Is there sufficient evidence to conclude that there is a difference in the average wear on the two types of tires? Use an appropriate hypothesis test to arrive at your condusion. b) (1 point) What assumptions are needed in order for our conclusion to be valid (i.e. what are the statistical assumptions needed for the test)? Question 2: Now let's assume that each automobile used both types of tires so we no longer have independent groups (i.e. the number of cars is 5, and all 5 cars use both tire types). a) (3 points) Is there now sufficient evidence to conclude that there is a difference in the average wear on the two types of tires? Use an appropriate hypothesis test to arrive at your conclusion. b) (1 point) What assumptions are needed in order for our conclusion to be valid (i.e. what are the statistical assumptions needed for the test)