In: Statistics and Probability
A manufacturing firm has adopted a new layout for its production process, which is intended to increase worker productivity. With the old layout, mean daily output was 200 units. A manager wants to test the null hypothesis that with the new layout, mean daily output is no greater than 200, against the alternative hypothesis that it is greater than 200. Assume that daily output levels are approximately normally distributed, with standard deviation 18 units.
The manager decides they will take a random sample of 81 days of output, and that when implementing the rejection region approach, they will use a critical value of 203. Calculate the maximum probability of Type I error. Four decimals