How do the results depend on the sample size?

Return to the Gallup Poll setting of Exercise 5.22.

We are supposing that the proportion of all adults who think that two children is ideal is p = 0.49.

What is the probability that a sample proportion

ˆp falls between 0.46 and 0.52 (that is, within ±3 percentage points of the true p) if the sample is an SRS of size n = 300? Of size n = 5000? Combine these results with your work in Exercise 5.22 to make a general statement about the effect of larger samples in a sample survey.