In constructing a confidence interval for the population mean when the population variance is unknown, which of the following assumptions is required when using the following formula? $$\bar { X } \pm t _ { a n , n - 1 } ( s / \sqrt { n } )$$
A)The sample size is greater than 30.
B)The population variance is known.
C)The population is normal.
D)The sample is drawn from a positively skewed distribution.

Question

Quizplus · Accepted Answer

The formula $\bar { X } \pm t _ { a n , n - 1 } ( s / \sqrt { n } )$ is used when the population variance is unknown, and it relies on the assumption that the population from which the sample is drawn is normally distributed. This is crucial for the validity of the t-distribution used in the formula.

In Constructing a Confidence Interval for the Population Mean When Xˉ±tan,n−1(s/n)\bar { X } \pm t _ { a n , n - 1 } ( s / \sqrt { n } )Xˉ±tan,n−1​(s/n​)

In Constructing a Confidence Interval for the Population Mean When $\bar { X } \pm t _ { a n , n - 1 } ( s / \sqrt { n } )$