Suppose that you perform a significance test and, based on the p-value, decide to reject the null hypothesis at the α = 0.05 significance level. Then suppose that your colleague decides to conduct the same test on the same data but using α = 0.10 as significance level. For the new significant level, would you reject the null hypothesis, fail to reject the null hypothesis, or would you not have enough information to say? (Hint: First ask yourself what must be true about the p-value based on your decision to reject the null hypothesis at the α = 0.05 significance level.)

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.)