A dairy farm uses the somatic cell count (SCC) report on the

milk it provides to a processor as one way to monitor the

health of its herd. The mean SCC from five samples of raw

milk was 250,000 cells per milliliter with standard deviation

37,500 cell/ml. Assume a normal distribution of SCC.

a. Construct the 90% confidence interval for the mean SCC of all milk

produced at the dairy.

b. Test whether these data provide sufficient evidence, at the 10% level

of significance, to conclude that the mean SCC of all milk produced at

the dairy exceeds that in the previous report, 210,250 cell/ml.

c.

Based on the test procedure in part b), find the power of the test when

the mean SCC of all milk produced at the dairy is 300,000 cell/ml.