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. SUVs equipped with tires using compound 1 have a mean braking distance of 41

41 feet and a standard deviation of 12.1

12.1 feet. SUVs equipped with tires using compound 2 have a mean braking distance of 47

47 feet and a standard deviation of 14.5

14.5 feet. Suppose that a sample of 78

78 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

1

1 be the true mean braking distance corresponding to compound 1 and

2

2 be the true mean braking distance corresponding to compound 2. Use the 0.1

0.1 level of significance.

Step 1 of 4: State the null and alternative hypotheses for the test.

Step 2 of 4: Compute the value of the test statistic. Round your answer to two decimal places.

Step 3 of 4: Determine the decision rule for rejecting the null hypothesis H₀. Round the numerical portion of your answer to two decimal places.

Step 4 of 4: Make the decision for the hypothesis test. Fail or reject to fail.