Chapter 6.12, Problem 3E

A new braking system is being evaluated for a certain type of car. The braking system will be installed if it can be conclusively demonstrated that the stopping distance under certain controlled conditions at a speed of 30 mi/h is less than 90 ft. It is known that under these conditions the standard deviation of stopping distance is approximately 5 ft. A sample of 150 stops will be made from a speed of 30 mi/h. Let μ represent the mean stopping distance for the new braking system.

1. a. State the appropriate null and alternate hypotheses.
2. b. Find the rejection region if the test is to be conducted at the 5% level.
3. c. Someone suggests rejecting H₀ if $\bar{X}\ge 89.4\text{ft}$. Is this an appropriate rejection region, or is something wrong? If this is an appropriate rejection region, find the level of the test. Otherwise explain what is wrong.
4. d. Someone suggests rejecting H₀ if $\bar{X}\le 89.4\text{ft}$. Is this an appropriate rejection region, or is something wrong? If this is an appropriate rejection region, find the level of the test. Otherwise explain what is wrong.
5. e. Someone suggests rejecting H₀ if $\bar{X}\le 89.4\text{ft}$ or if $\bar{X}\ge 90.6\text{ft}$. Is this an appropriate rejection region, or is something wrong? If this is an appropriate rejection region, find the level of the test. Otherwise explain what is wrong.