Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. A marketing director for a beverage company conducted a study to investigate people’s soda preferences in two regions of the country. The director selected a random sample of 100 people from the east coast and a random sample of 100 people from the west coast to survey. The responses are summarized in the following table.

East CoastWest Coast
Regular soda4437
Diet soda3942
No preference1721
Total100100
Do the data provide convincing statistical evidence, at the level of α=0.05, that the preferences are different between the two regions of the country? Complete the appropriate inference procedure to support your answer.

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.)