A transportation engineer conducted a series of tests to demonstrate that a new cement mix for highway construction will withstand 25 years of service. She develops a wear index (WI) to assess the status of a sample after a demanding set of tests. A mix will be acceptable if its wear index has a mean value less than 20 on a scale of 0-100. Fifteen sample values of the wear index appeared to be normally distributed with a sample mean of 18.31 and a sample standard deviation of 3.09. A. Specify the appropriate null and alternative hypotheses to demonstrate that the mix does meet the target value of 20.
B. What is the rejection region for a 5% test?
C. What do you conclude for this data set?