In: Statistics and Probability
To test the ability of auto mechanics to identify engine problems, an automobile with a single engine problem was taken to 72 different auto repair shops. 42 of the 72 mechanics who worked on the car correctly identified the problem. Is there evidence to suggest that the true proportion of mechanics who could correctly identify this problem is less than 0.75?
(a) Set up the null and alternative hypotheses.
(b) Conduct the hypothesis test at α = 0.01. Clearly specify the distribution used, critical value, test statistic, and decision in context of the problem.