This problem is from “The basic practice of statistics,Moore, 4th edition, quest

Question

This problem is from “The basic practice of statistics,Moore, 4th edition, question 8:50”

Your help in answering this question is appreciated.

A New York Times News service article on a poll concerned withthe opinions of Hispanics included this paragraph:

The poll was conducted by telephone from July 13 to 27, with3092 adults nationwide, 1074 whom described themselves asHispanics. It has a margin of sampling error of plus or minus threepercentage points for the entire poll and plus or minus fourpercentage points for Hispanics. Sample sizes for most Hispanicnationalities, like Cubans or Dominicans, were too small to breakout the results separately.

a) Why is he "margin of sample error" larger for Hispanics thanfor all 3092 respondents?

b) Why would a very small sample size prevent a responsible newsorganization from breaking out results for Cubans separately?

Explanation / Answer

a) because the sample size for Hispanics is about 1/3 of the totalsample size b) because the conditions for creating a confidence interval mightnot be satisfied with a small sample

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