Question

A consumer advocacy group is doing a large study on car rental practices. Among other things, the consumer group would like to do a statistical test regarding the mean monthly mileage, μ, of cars rented in the U.S. this year. The consumer group has reason to believe that the mean monthly mileage of cars rented in the U.S. this year is less than last year's mean, which was 2850 miles. The group chooses a random sample of 50 cars rented in the U.S. this year and records their monthly mileages. Suppose that the population of monthly mileage of cars rented in the U.S. this year has a standard deviation of 800 miles and that the group performs its hypothesis test using the 0.05 level of significance

Based on this information, answer the questions below. Carry your intermediate computations to at least four decimal places, and round your responses as indicated.

1. What are the null and alternative hypothesis that the group should us for the test?

2. What is the probability that the group commits a type I error? Round to 2 decimal places

3. Assuming that the actual value of U is 2541 miles, what is the power of the test? Round to two decimals

4. Suppose that the group decides to perform another statistical test using the same population, the same null and alternative hypothesis, and the same level of significance, but for this second test the group chooses a random sample of size 75 instead if a random sample of size 50. Assuming that the actual value of U is 2541 miles, how does the probability that the group commits a type II error in this second test compared to the probability that the group commits a type II error in the original test? ANSWERS: A) the probability of committing a type II error in the second test is greater. B) The probability of committing a type II error in the second test is less. C) The probabilities of committing a type II error are equal.

Answer 1