You are to establish a procedure for measuring the radioactivity of samples placed in a counter. The calibration of the counter is such that one net count in the allotted time corresponds to 2.27 Bq of sample activity. The expected number of background counts, B = 1080, during the allotted time is accurately known. The acceptable risk for making a type-I error is 5% and that for a type-II error, 1%.

a) What is the minimum significant net sample count?

b) What is the minimum significant measured activity?

c) What is the minimum detectable true activity?

d) A certain sample-plus-background reading registers 1126 gross counts. What is the implied sample activity?

e) What would be the answer to (d) if one were willing to risk a type-I error in 10% of the measurements?

f) With the type-I error probability set at its original value of 5%, what would be the minimum detectable true activity if one were to accept a 10% (instead of 1%) risk of a type-II error?