Determine whether the given conditions justify using the margin of error $\mathrm { E } = \mathrm { z } _ { \alpha / 2 } \sigma / \sqrt { \mathrm { n } }$ when finding a confidence interval estimate of the population mean $\mu$.
-The sample size is $\mathrm { n } = 10$ and $\sigma$ is not known.
A) No
B) Yes

Question

Quizplus · Accepted Answer

The formula $E = z_{\alpha/2} \sigma / \sqrt{n}$ requires that the population standard deviation $\sigma$ is known and that the sample size is large (usually $n \geq 30$) or the population is normally distributed. Since $\sigma$ is not known and the sample size is small ($n = 10$), this formula is not appropriate.

Determine Whether the Given Conditions Justify Using the Margin of Error