An engineer must report as to the kind of soil-pile behavior that exists at a site. The choice will be based on the indications from the blow counts from five preliminary piles. The null hypothesis is that the behavior is type A which is known from experience to exhibit a mean blow count of 20/ft, while the alternate hypothesis is that the behavior is type B, which gives rise to a mean blow count of 30/ft. In both cases the standard deviation of the number of blows per foot is 5.

(a) Propose a logical hypothesis test, i.e., a logical statistic and a reasonable form for the operating rule.

(b) Find the specific operating rule which gives a type I error probability of 25 percent. Assume an appropriate, convenient distribution for the sample statistic adopted.

(c) What is the β probability for the test?

(d) What should the engineer report if the blow counts observed are 31, 22, 28, 25, 32?