6. A survey of New York City residents is performed using cluster sampling. The design effect is 3.0. From the survey, the estimated proportion who prefer the Mets to the Yankees is 0.42 with a standard error of 0.05. How many people were in the sample?
Solution to question 5
From yesterday:
5. Which of the following better describes changes in public opinion on most issues? (Choose only one.)
(a) Dynamic stability: On any given issue, average opinion remains stable but liberals and conservatives move back and forth in opposite directions (the “accordion model”)
(b) Uniform swing: Average opinion on an issue can move but the liberals and conservatives don’t move much relative to each other (the disribution of opinions is a “solid block of wood”)
(c) Compensating tradeoffs: When considering multiple survey questions on the same general topic, average opinion can move sharply to the left or right on individual questions while the average over all the questions remains stable (the “rubber band model”)
Solution: b. You can make an argument for option a over the long term, but if you have to pick just one of the three, you have to go with uniform swing.
Question 1 turned out to be a nice example for something I was putting together about nuisance parameters, which I just put up.
Just wanted to say thanks for the inspiration :)
292? I had to look up what “design effect” is and took as some sort of correction factor for the sample size estimate between cluster and cluster sampling. If so, the rest is easy:
0.05=sqrt(n*0.42*(1-0.42))/n
n=97.44 and 3X that is ~ 292
Umm, I meant “between random and cluster sampling”. Also, “took it as …”
Hehe, “easy”. Got both SD and SE formulas wrong. What an embarrassment. Hopefully this gets it right:
0.05=sqrt(0.42*(1-0.42)/n)/sqrt(n) from which n ~9.87. And 3X of that is ~ 30. So the survey was 30 people. (???)
DK, I think you were right the first time.
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