Question: A coalmining company suspects that certain detonators used with explosives do not meet the requirement that at least 90% will ignite. To test the hypothesis

A coalmining company suspects that certain detonators used with explosives do not meet the requirement that at least 90% will ignite. To test the hypothesis H0 : p = 0.9 vs Ha : p < 0.9, a random sample of n = 20 detonators is selected and tested. Let X denote the number of those that ignite. For each of the two rejection rules Rule 1: X ≤ 16 and Rule 2: X ≤ 17,

(a) calculate the probability of type I error, and

(b) calculate the probability of type II error when the true value of p is 0.8.

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