The heat evolved in calories per gram of a cement mixture is approximately normally distributed. The mean is thought to be 100, and the standard deviation is 4. You wish to test H0: = 100 versus H1: < 100. Use sample size n = 10.

(a) If the acceptance region is defined as 97.5, find the type I probability error . (b) Find error for the case in which the true mean heat evolved is 103. (c) Find error for the case in which the true mean heat evolved is 105. This value of error Is smaller than the one found in part (b). why?