Question: A company manufactures particle board whose breaking strength has a mean of 100 lbs and a standard deviation of 28 lbs. It is believed that by a newly developed process the mean breaking strength can be increased.

a) If, under the new process, 100 boards are tested and the average breaking strength was found to be 104 lbs, can we conclude that the new process is better? Assume a level of significance of .01 and the standard deviation is still 28 lbs.

b) What is the probability of accepting the old process when in fact the new process has increased the mean breaking strength to 110? Is this a Type I or II error? Calculate the other.

c) Suppose we use a sample size of 150. Is the new Type I error larger or smaller? Is the new Type II error larger or smaller?

d) Suppose 106 is the critical value. Is the new Type I error larger or smaller? Is the new Type II error larger or smaller?