Question

independent practice
determine the standard deviation of the sampling distribution if the
populations standard deviation is $43.7 and samples of size $n = 15$ are
collected.
$0.19
$43.7
$2.91
$11.28

Explanation:

Step1: Recall the formula for standard deviation of sampling distribution

The formula for the standard deviation of the sampling distribution (also known as the standard error) is \(\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}\), where \(\sigma\) is the population standard deviation and \(n\) is the sample size.

Step2: Substitute the given values into the formula

Given \(\sigma = 43.7\) and \(n = 15\). Then \(\sigma_{\bar{x}}=\frac{43.7}{\sqrt{15}}\).
First, calculate \(\sqrt{15}\approx3.87298\).
Then \(\sigma_{\bar{x}}=\frac{43.7}{3.87298}\approx11.28\)

Answer:

\(\$11.28\)