A highway construction zone has a posted speed limit of 40 miles per hour. Workers working at the site claim that the mean speed of vehicles passing through this construction zone is at least 50 miles per hour. A random sample of 36 vehicles passing through this zone produced a mean speed of 48 miles per hour. The population standard deviation is known to be 4 miles per hour.
a. Do you think the sample information is consistent with the workers’ claim? Use α = .025.
b. What is the Type I error in this case? Explain. What is the probability of making this error?
c. Will your conclusion of part a change if the probability of making a Type I error is zero?
d. Find the p-value for the test of part a. What is your decision if α = .025?