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. the mean braking distance for suvs equipped with tires made with compound 1 is 74 feet, with a population standard deviation of 13.4. the mean braking distance for suvs equipped with tires made with compound 2 is 77 feet, with a population standard deviation of 14.3. suppose that a sample of 41 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 $mu_1$ be the true mean braking distance corresponding to compound 1 and $mu_2$ be the true mean braking distance corresponding to compound 2. use the 0.05 level of significance. step 1 of 5: state the null and alternative hypotheses for the test.

Explanation:

Step1: Define null hypothesis

The null hypothesis $H_0$ is a statement of no - effect or no difference. Here, we assume that the mean braking distance of compound 1 is not less than that of compound 2. So, $H_0:\mu_1-\mu_2\geq0$.

Step2: Define alternative hypothesis

The alternative hypothesis $H_a$ is the claim we are trying to find evidence for. The claim is that the braking distance for SUVs equipped with tires using compound 1 is shorter than when compound 2 is used. So, $H_a:\mu_1 - \mu_2<0$.

Answer:

$H_0:\mu_1-\mu_2\geq0$
$H_a:\mu_1 - \mu_2<0$