percentage of plate appearances by a baseball player that the ball is put in pla

Question

percentage of plate appearances by a baseball player that the ball is put in play (as opposed to striking out). Historically, the average has been 80%. Suppose one wants to test that this rate has not changed during the last season by randomly selecting 260 plate appearances by players and recording the percentage of players that put the ball in play. using = 0.05, complete parts a through c below. a. Explain how Type I and Type ll errors can occur in this hypothesis A Type I error can occur if the proportion of plate appearances that result in the ball being put in play | 0.80 and the null hypothesis | A Type II error can occur if the proportion of plate | 080 appearances that result in the ball being put in the play and the null hypothesis b. Calculate the probability of a Type Il error occurring if the actual contact rate is 76%. The probability of committing a Type ll error is Round to four decimal places as needed.) is 90%. The probability of committing a Type ll error is (Round to four decimal places as needed.)

Explanation / Answer

a)
A type I error can occur if the proportion of plate appearances that result in the ball being put in play is equal to 0.80 and the null hypothesis is rejected.
A type II error can occur if the proportion of plate appearances that result in hte ball being put in the play is not equal to 0.80 and the null hypothesis is not rejected.

b)

c)

p0 (hypothesised proportion) 0.8 SE = sqrt(p*(1-p)/n) 0.02480695 n 260 alpha 0.05 sample/true proportion 0.76 Std. Error. SE 0.0248 Zcritical 1.645 Xcritical 0.84 0.7591962 Beta or type II error is the probability of fail to reject the null hypothesis P(p>0.84) 0.0006 P(p<0.76) 0.4871 Hence type II error probability is 0.4876

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