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 77 feet and a standard deviation of 12.8 feet. SUVs equipped with tires using compound 2 have a mean braking distance of 85 feet and a standard deviation of 5.3 feet. Suppose that a sample of 33 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 0.1 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. = reject? or fail to reject?

Answer #1

To Test :-

H0 :-

H1 :-

Test Statistic :-

t = -3.3172
-3.32

Test Criteria :-

Reject null hypothesis if

DF = 42

Result :- Reject Null Hypothesis

Conclusion :- Accept Alternative hypothesis

There is sufficient evidence to support the claim that compound 1 is shorter than the braking distance when compound 2 is used at 10% level of significance

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