A researcher compares two compounds(1 and 2) used in the manufacture of car tires that are designed to reduce braking distances for SUVs equipped with the tires The mean braking distance for SUVs equipped with tires made with compound 1 is 53 feet, with a population standard deviation of 8.2. The mean braking distance for SUVs equipped with tires made with compound 2 is 59 feet, with a population standard deviation of 12.1 Suppose that a sample of 47 braking tests are performed for each compound. Using these results, test the claim that the braking distance for SUVs equipped with tires using compound 1 is shorter than the braking distance when compound 2 is used. Let u1 be the true mean braking distance corresponding to compound 1 and u2 be the true mean braking distance corresponding to compound 2. Use the 0.01 level of significance.

1. state the null and alternative hypotheses for the test

Ho: u1-u2_____________0 Ha: u1-u2___________0

2. compute the value of the test statistic. (round 2 decimal places)

3. Find the P value associated with the test statistic (Round 4 decimal places)

4. Make the decision for the hypothesis test.

(1. reject Null hypothesis 2.. Fail to reject Null hypothesis)

5. State the conclusion of the hypothesis test

(1. There is sufficient evidence to support. 2. There is not sufficient evidence)