A recent poll asked a random sample of 1012 U.S. adults what they do with the milk in the bowl after they have eaten the ceral. Of the respondents, 67% said that they drink it. Suppose that 70% of U.S adults actually drink the ceral milk. Let p be the proportion in the sample who drink ceral milk.
1) What is the mean of the sampling distribution of p? Why?
2) Find the standard deviation of the sampling distribution of p. Check to see if the 10% condition is met.
3) Is the sampling distribution of p approximately Normal? Check to see if the Normal condition is met.
4) Find the probability of obtaining a sample of 1012 adults in which 67% or fewer say they drink the cereal milk. Do you have any doubts about the results of this poll?
5) What sample size would be required to reduce the standard deviation of the sampling distribution to one-half the value you found above. Justify your answer.