Question

Testing the Difference Between Two Means In Exercises 15–24, (a) identify the claim and state H0, and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic z, (d) decide whether to reject or fail to reject the null hypothesis and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed.

15. Braking Distances To compare the dry braking distances from 60 to 0 miles per hour for two makes of automobiles, a safety engineer conducts braking tests for 23 models of Make A and 24 models of Make B. The mean braking distance for Make A is 137 feet. Assume the population standard deviation is 5.5 feet. The mean braking distance for Make B is 132 feet. Assume the population standard deviation is 6.7 feet. At a = 0.10, can the engineer support the claim that the mean braking distances are different for the two makes of automobiles?

Answer 1

Claim:

At alpha = 0.10, the critical values are +/- z_0.05 = +/- 1.645

Reject H₀, if z < -1.645 or, z > 1.645

The test statistic is

  

Since the test statistic value is greater than the positive critical value(2.80 > 1.645), so we should reject the null hypothesis.

At 0.10 significance level, there is sufficient evidence to support the claim that the mean breaking distances are different for the two makes of automobiles.