Question

1. The standard recommendation for automobile oil changes is once every 5000 miles. A local mechanic is interested in determining whether people who drive more expensive cars are more likely to follow the recommendation. Independent random samples of 45 customers who drive luxury cars and 40 customers who drive compact lower-price cars were selected. The average distance driven between oil changes was 5187 miles for the luxury car owners and 5389 miles for the compact lower-price car owners. The sample standard deviations were 424 and 507 miles for the luxury and compact groups, respectively. Assume that the two population distributions of the distances between oil changes have the same standard deviation. You would like to test if the mean distance between oil changes is less for all luxury cars than that for all compact lower-price cars.

Let μ₁ denote the mean distance between oil changes for luxury cars, and μ₂ denote the mean distance between oil changes for compact lower-price cars. Calculate the appropriate statistic for this test. Round your intermediate calculations (all standard deviations) as well as your final answer to the nearest hundredth.

2. A local college cafeteria has a self-service soft ice cream machine. The cafeteria provides bowls that can hold up to 16 ounces of ice cream. The food service manager is interested in comparing the average amount of ice cream dispensed by male students to the average amount dispensed by female students. A measurement device was placed on the ice cream machine to determine the amounts dispensed. Random samples of 85 male and 78 female students who got ice cream were selected. The sample averages were 7.23 and 6.49 ounces for the male and female students, respectively. Assume that the population standard deviations are 1.22 and 1.17 ounces, respectively. You would like to test whether the average amount of ice cream dispensed by all make college students is different from the average amount dispensed by all female college students.

a. Let μ1 denote the average amount of ice cream dispensed by all male college students, and μ2 denote the average amount of ice cream dispensed by all female college students. Calculate an appropriate test statistic for this case. Round your intermediate calculations to the nearest ten thousandth and round your final answer to the nearest hundredth.

b. Let μ1 denote the average amount of ice cream dispensed by all male college students, and μ2 denote the average amount of ice cream dispensed by all female college students. Suppose the test statistic associated to this test is 3.95. Calculate the p-value. Round your answer to the nearest ten thousandth (e.g., 0.1234).

Answer 1

Thank you!