Contact rate is defined as the percentage of plate appearances by Major League Baseball players that the ball is put in play (as opposed to striking out). Historically, the Major League average has been 80%. Suppose we want to test that this rate has not changed recently by randomly selecting 250 plate appearances by players and recording the percentage of players that put the ball in play. Using σ = 0.05, answer the following questions:
a. Explain in your own words how Type I and Type II errors can occur in this hypothesis test.
b. Calculate the probability of a Type II error occurring if the actual contact rate is 77%.
c. Calculate the probability of a Type II error occurring if the actual contact rate is 88%.