Let the pmf of the population x be p(x = k) = p(1 − p) k−1 (k = 1, 2, 3, . .) with the parameter p, 0 < p < 1. (geometric distribution.) we take a sample of size n = 1. the hypothesish0 says p ≥ 0.05, whereas h1 claims p < 0.05. find a level α = 0.02 ump hypothesis test. calculate the power of the test.

Afriend of mine is giving a dinner party. his current wine supply includes 10 bottles of zinfandel, 8 of merlot, and 11 of cabernet (he only drinks red wine), all from different wineries. (a) if he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? ways (b) if 6 bottles of wine are to be randomly selected from the 29 for serving, how many ways are there to do this? ways (c) if 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety? ways (d) if 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? (round your answer to three decimal places.) (e) if 6 bottles are randomly selected, what is the probability that all of them are the same variety? (round your answer to three decimal places.)