National Motors has equipped the ZX-900 with a new disk brake system. We define m to be
Question:
National Motors has equipped the ZX-900 with a new disk brake system. We define m to be the mean stopping distance (from a speed of 35 mph) of all ZX-900s. National Motors would like to claim that the ZX-900 achieves a shorter mean stopping distance than the 60 ft claimed by a competitor.
a. Set up the null and alternative hypotheses needed to support National Motors’ claim.
b. A television network will allow National Motors to advertise its claim if the appropriate null hypothesis can be rejected at α = .05. If a random sample of 81 ZX-900s have a mean stopping distance of 57.8 ft, will National Motors be allowed to advertise the claim? Assume that the population standard deviation equals 6.02 ft and justify your answer using both a critical value and a p-value.
Step by Step Answer:
a 1 State the Hypotheses and what each represents H 0 60 no improvement in average stopping distances from 35 mph H a 60 the new disk brake system achieves stopping distances averaging shorter than 60 b 2 State the Level of Significance OneSided 05 3 Select which Test Statistic to use to test Hypotheses about the Population Parameter We will use z to test Hypotheses about because is known and x is approximately normal since n 81 is large enough to apply the Central Limit Theorem Critical Value Method 4 Determine the Critical Value and State the Decision Rule The critical value z 05 1645 Reject the null hypothesis if the test statistic is less than 1645 5 Compute the Test Statistic from the Sample Data The test statistic z x x s x 578 6006689 2206689 32890 Make the Decision to RejectNot Reject H0 and Interpret the results with respect to the specific problem Because the test statistic of 32890 is less than 1645 the test statistic is in the critical region so we do reject the null hypothesis in favor of the alternative We conclude that there is strong evidence that the average stopping distance ...View the full answer
Essentials Of Business Statistics
ISBN: 9780078020537
5th Edition
Authors: Bruce Bowerman, Richard Connell, Emily Murphree, Burdeane Or
