# Question: Let p denote the probability that for a particular tennis

Let p denote the probability that, for a particular tennis player, the first serve is good. Since p = 0.40, this player decided to take lessons in order to increase p. When the lessons are completed, the hypothesis H0: p = 0.40 will be tested against H1: p > 0.40 on the basis of n = 25 trials. Let y equal the number of first serves that are good, and let the critical region be defined by C = {y : y ≥ 13}.

(a) Determine α = P(Y ≥ 13; p = 0.40). Use Table II in the appendix.

(b) Find β = P(Y < 13) when p = 0.60; that is, β = P(Y ≤ 12; p = 0.60).

(a) Determine α = P(Y ≥ 13; p = 0.40). Use Table II in the appendix.

(b) Find β = P(Y < 13) when p = 0.60; that is, β = P(Y ≤ 12; p = 0.60).

## Answer to relevant Questions

It was claimed that 75% of all dentists recommend a certain brand of gum for their gum-chewing patients. A consumer group doubted this claim and decided to test H0: p = 0.75 against the alternative hypothesis H1: p < 0.75, ...Data were collected during a step-direction experiment in the biomechanics laboratory at Hope College. The goal of the study is to establish differences in stepping responses between healthy young and healthy older adults. ...Let X1, X2, X3 be a random sample of size n = 3 from an exponential distribution with mean θ > 0. Reject the simple null hypothesis H0: θ = 2, and accept the composite alternative hypothesis H1: θ < 2, if the observed sum ...Consider a random sample X1, X2, . . . , Xn from a distribution with pdf f(x; θ) = θ(1 − x)θ−1, 0 < x < 1, where 0 < θ. Find the form of the uniformly most powerful test of H0: θ = 1 against H1: θ > 1. It has been claimed that, for a penny minted in 1999 or earlier, the probability of observing heads upon spinning the penny is p = 0.30. Three students got together, and they would each spin a penny and record the number X ...Post your question