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Do you go to church? The Gallup Poll asked a random sample of 1785 adults whether they
Chapter 7, Problem 36(choose chapter or problem)
Do you go to church? The Gallup Poll asked a random sample of 1785 adults whether they attended church during the past week. Let \(\hat{p}\) 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 \(\hat{p}\)? Why?
(b) Find the standard deviation of the sampling distribution of \(\hat{p}\). Check to see if the 10% condition is met.
(c) Is the sampling distribution of \(\hat{p}\) 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
Questions & Answers
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 \(\hat{p}\) 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 \(\hat{p}\)? Why?
(b) Find the standard deviation of the sampling distribution of \(\hat{p}\). Check to see if the 10% condition is met.
(c) Is the sampling distribution of \(\hat{p}\) 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
ANSWER:Step 1 of 4
a)
Given:
The mean of the sampling distribution of the sample proportion 
Because the sample proportion is an unbiased estimator for the population proportion.
Step 2 of 4
b)
Given:
The standard deviation of the sampling distribution of the sample proportion