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 n = 286 and $\sigma = 15$
A)Yes
B)No

Question

Quizplus · Accepted Answer

The formula $E = z_{\alpha/2} \sigma / \sqrt{n}$ is appropriate for finding a confidence interval estimate of the population mean $\mu$ when the population standard deviation $\sigma$ is known and the sample size $n$ is large (n ≥ 30 is a common rule of thumb). Here, $\sigma = 15$ is known and $n = 286$, which is much larger than 30, justifying the use of this formula.

Determine Whether the Given Conditions Justify Using the Margin of Error