You randomly draw a sample of n = 9 where $\sigma$ = 4. If the sample mean is 1, which of the following are the bounds of a 99% confidence interval?
A) -3.47, 5.47
B) -5.47, 3.47
C) -3.33, 5.33
D) -5.33, 3.33

Question

Quizplus · Accepted Answer

The correct answer is A because the bounds of a 99% confidence interval are given by the sample mean plus or minus the margin of error, which is equal to the critical value times the standard error of the mean. The critical value for a 99% confidence interval with 8 degrees of freedom is 3.47, and the standard error of the mean is 1/sqrt(9) = 1/3. Therefore, the bounds of the confidence interval are 1 +/- 3.47 * 1/3 = -3.47, 5.47.

You Randomly Draw a Sample of N = 9 Where σ\sigmaσ

You Randomly Draw a Sample of N = 9 Where $\sigma$