10
QuizMultiple Choice

More about Confidence Intervals

Question 10 • CA-Statistics and Probability B

An animal rescue agent wanted to estimate the true proportion of all animals in shelters that are adopted each month. To do so, she selects a random sample of 100 animals that were in shelters last month and determines that the 95% confidence interval for the true proportion of animals adopted is between 0.12 and 0.24. This interval has a margin of error of 0.06. Which of the following can be accounted for by the margin of error?

Answer
A
response bias
B
nonresponse bias
C
sampling variation
D
undercoverage bias

Explanation

A margin of error describes the uncertainty in an estimate that comes from using a random sample instead of every animal in the population. Here, the sample proportion is 0.18, and the margin of error of 0.06 reflects sampling variation around that estimate. Response bias, nonresponse bias, and undercoverage bias are systematic problems with how data are collected, and a margin of error does not account for them. The correct choice is sampling variation.

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