Question: Do you drink the cereal milk? A USA Today Poll asked a random sample of 1012 U.S. adults what they do with the milk in the bowl after they have eaten the cereal. Let p^ be the proportion of people in the sample who drink the cereal milk. A spokesman for the dairy industry claims that 70% of all U.S. adults drink the cereal milk. Suppose this claim is true.
(a) What is the mean of the sampling distribution of p^? Why?
(b) Find the standard deviation of the sampling distribution of p^. Check to see if the 10% condition is met.
(c) Is the sampling distribution of p^ approximately Normal? Check to see if the Large Counts condition is met.
(d) Of the poll respondents, 67% said that they drink the cereal milk. Find the probability of obtaining a sample of 1012 adults in which 67% or fewer say they drink the cereal milk if the milk industry spokesman's claim is true. Does this poll give convincing evidence against the claim? Explain.