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? $\bar { x } \pm t _ { n / 2 } \frac { s } { \sqrt { n } }$
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 for constructing a confidence interval for the population mean when the population variance is unknown requires the assumption that the population is normal. This is because the formula uses the standard deviation of the sample (s) as an estimate for the standard deviation of the population (which is unknown) and relies on the t-distribution, which is only appropriate when the population is normal or the sample size is large (greater than 30).

In Constructing a Confidence Interval for the Population Mean When xˉ±tn/2sn\bar { x } \pm t _ { n / 2 } \frac { s } { \sqrt { n } }xˉ±tn/2​n​s​

In Constructing a Confidence Interval for the Population Mean When $\bar { x } \pm t _ { n / 2 } \frac { s } { \sqrt { n } }$