I just need part b). Please explain fully. Let p denote the probability that, fo

Question

I just need part b). Please explain fully.

Let p denote the probability that, for a particular tennis player, the first serve is good. Since p=0.4, this player decided to take lesson in order to increase p. When the lesson are completed, the hypothesis H0 =0.4 will be tested against Ha > 0.4 on the basis of n=25 trails. Let y equal the number of first servers that are good , and let the critical region be defined by C={y:y is greater than or equal to 13}. (a) Determine the level of significance (Type I error) using Table II. (b) Find Type II error when p=0.60.

Explanation / Answer

Type 2 error = P(X <= 12|p = .6), as we will then fail to reject the null hypothesis.

In Excel, this is simply binomdist(12,25,.6,TRUE) = 0.153767768975763

I will do a just for the heck of it P(X>= 13|p=.4) = 1 - P(X<=12|p=.4) =

1 - binomdist(12,25,.4,TRUE) = 0.153767768975763

You might wonder why the answers are the same. Note the mirror image nature of this problem.

we go from p = .4 to p = .6 = 1- .4 and region P(X >= 13) with 25 values to P(X <= 12) = P(X <= 25-13)

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