According to the Pew Research Center*, as of 2008 approximately 26.3% of Americans identified with Evangelical Protestant denominations. The figures below show potential sampling distributions for the proportion of a sample who identify as Evangelical Protestants for samples of size n=50, n=100, and n=1000.

a. Which sampling distribution corresponds to a sample size of n=50, n=100, and n=1000?

b. If we use a proportion, to estimate the population parameterp=0.263, would it be very surprising to get an estimate that is off by more than 0.35 (that is, the sample proportion is less than 0.228 or greater than 0.298) if we had samples of size n=50? What if we had samples of n=100? And what if we had samples of n=1000?

c. What is the shape, center, and spread for each of the sampling distributions?

d. In terms of shape, center, and spread, what do these sampling distributions have in common? How do they differ?

e. What does each dot in each dotplot represent?

Figure A (n =50) Left Tail Two-Tail Right Tail samples = 1000 125 mean = 0.263 std. error = 0.061 100 75 50 25 0. 10 0.15 0.20 0.25 1 0.30 0.35 0.40 0.263 0.45 Figure B (n=100) 100 Left Tail Two-Tail Right Tail samples = 1000 mean = 0.263 std. error = 0.044 30 60 40 20 0. 15 0.20 0.25 0.30 0.35 0.263