Question: Do you go to church? The Gallup Poll asked a random sample of 1785 adults whether they attended church during the past week. Let p^ be the proportion of people in the sample who attended church. A newspaper report claims that 40% of all U.S. adults went to church last week. 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, 44% said they did attend church last week. Find the probability of obtaining a sample of 1785 adults in which 44% or more say they attended church last week if the newspaper report's claim is true. Does this poll give convincing evidence against the claim? Explain.