A company makes 4K monitors and does not like to have defective pixels. Historically, the mean number of defective pixels in a TV is 20. An engineer is hired to make better monitors that have fewer defective pixels. After her first week of work she claims that she can significantly improve the current method. To check her claim you try her new method on 100 new monitors. The average number of defective pixels in those 100 monitors is 19.1. Assume that the new method doesn't change the standard deviation of defective pixels, which has always been 4.

(a) Test if the new method is significantly better than the old one at the α = 0.05 level.

(b) Using the new method, assume that the mean number of defective pixels is actually 19. What is the chance that your test from part 1 will conclude that the new method is statistically more effective?

(c) How many monitors will you have to check so that the test you did in part A will conclude that the new method is effective, with 95% probability? Please assume again that the mean number of defective pixels is actually 19.