The Gallup Poll asked a random sample of 1785 adults if they attended church during the past week. Let p̂ 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 p̂?

b. Find the standard deviation of the sampling distribution of p̂. Verify that the 10% condition is met.

c. Verify that the sampling distribution of p̂ is approximately Normal.

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, assuming the newspaper report’s claim is true.

e. Does this poll give convincing evidence against the newspaper’s claim? Explain your reasoning.