Question

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 62 feet and a standard deviation of 10.5 feet. SUVs equipped with tires using compound 2 have a mean braking distance of 66 feet and a standard deviation of 12.0 feet. Suppose that a sample of 86 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 μ1 be the true mean braking distance corresponding to compound 1 and μ2 be the true mean braking distance corresponding to compound 2. Use the 0.05 level of significance.

Step 1: State the null and alternative hypotheses for the test Step2: Compute the value of the test statistic. Round your answer to two decimal places Step 3: Determine the decision rule for rejecting the null hypothesis Ho. Round the numerical portion of your answer to two decimal places Step 4: Make the decision for the hypothesis test

Answer 1

Let denote the average braking distance for SUVs equipped with tires using compound 1 and compound 2 respectively.

Conclusion in the context of the problem :

There is sufficient evidence to support 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.