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

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### Comparison of Tire Compounds in Reducing Braking Distances

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.

- **Compound 1**: Tires using this compound have a mean braking distance of 55 feet and a standard deviation of 14.0 feet.
- **Compound 2**: Tires using this compound have a mean braking distance of 58 feet and a standard deviation of 13.7 feet.

Using these results, suppose that a sample of 81 braking tests are performed for each compound. The study aims to 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 4: State the Null and Alternative Hypotheses for the Test

- **Null Hypothesis (\( H_0 \))**: \( \mu_1 = \mu_2 \)
- **Alternative Hypothesis (\( H_a \))**: \( \mu_1 < \mu_2 \)

You can input your answer using the provided keyboard shortcuts. After completing the step, click "Submit Answer" to proceed.

For further reference, check the tables and keypad options available.
Transcribed Image Text:### Comparison of Tire Compounds in Reducing Braking Distances 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. - **Compound 1**: Tires using this compound have a mean braking distance of 55 feet and a standard deviation of 14.0 feet. - **Compound 2**: Tires using this compound have a mean braking distance of 58 feet and a standard deviation of 13.7 feet. Using these results, suppose that a sample of 81 braking tests are performed for each compound. The study aims to 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 4: State the Null and Alternative Hypotheses for the Test - **Null Hypothesis (\( H_0 \))**: \( \mu_1 = \mu_2 \) - **Alternative Hypothesis (\( H_a \))**: \( \mu_1 < \mu_2 \) You can input your answer using the provided keyboard shortcuts. After completing the step, click "Submit Answer" to proceed. For further reference, check the tables and keypad options available.
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