A researcher finds that the 13 Muslims surveyed in the 2008GSS had a mean of 2.38 children with a standard deviation of 2.10. With this information, she builds a confidence interval for the Muslim population's number of children: 1.05 ≤ μ ≤ 3.71. Which confidence interval is she using?
A) 90%
B) 95%
C) 99%
D) 99.9%

Question

Quizplus · Accepted Answer

Working backwards, we know that the researcher added and subtracted 1.33 to and from the sample mean of 2.38. The value of the estimate of the standard error is .61 (2.10 divided by the square root of 12). So, .61 multiplied by some number is 1.33. This number must be 2.18, and in the t-table, with 12 degrees of freedom, this matches up to .025. .025 + .025 = .05, therefore it is a 95% confidence interval.

A Researcher Finds That the 13 Muslims Surveyed in the 2008GSS