An engineer measured the brinell hardness of 25 pieces of ductile iron that were subcritically annealed. the sample average was found to be =172.52. the engineer needs to test if the mean brinell hardness of all such ductile iron pieces is greater than 170. assume that brinell hardness is normally distributed with standard deviation of ? ? =10.

a. write down the null and alternative hypotheses to be tested.

b. test the hypotheses at ? ? =0.05, using the test statistic approach. what is your decision on null )? interpret the test results.

c. construct a 95% confidence interval for the mean brinell hardness. test the hypotheses using the confidence interval method. do you get the same answer as in part (b)?

d. what is the ? ? for the test? test the hypotheses using the ? ? do you get the same answer as parts (b) and (c)?