The Gallup organization frequently conducts polls in which they ask the following question:
“In general, do you feel that the laws covering the sale of fire-arms should be made more strict, less strict, or kept as they are now?”
In February 1999, 60% of those surveyed said “more strict,” and on April 26, 1999, shortly after the Columbine High School shootings, 66% of those surveyed said “more strict.”
a. Assume that both polls used samples of 560 people. Determine the number of people in the sample who said “more strict” in February 1999, before the school shootings, and the number who said “more strict” in late April 1999, after the school shootings.
b. Do a test to see whether the proportion that said “more strict” is statistically significantly different in the two different surveys, using a significance level of 0.01.
c. Repeat the problem, assuming that the sample sizes were both 1120.
d. Comment on the effect of different sample sizes on the p-value and on the conclusion.