The heat evolved in calories per gram of a cement mixture is approximately normally distributed. the mean is thought to be 101.1 and the standard deviation is 5.8. we wish to test upper h subscript 0 baseline colon mu equals 101.1 versus upper h subscript 1 baseline colon mu not-equals 101.1 with a sample of n=9specimens.
(a) if the acceptance region is defined as 98< xbar< 102, find the type 1 error probability α.
(b) find β for the case where the true mean heat evolvedis 103.
(c) find β for the case where the true mean heat evolvedis 105. this value of β is smaller than the one found in part(b) above. why?