Question

if samples of size 800 are selected from a population, then calculate the standard error of the distribution of sample means, based on a sample with a mean of 266 and a standard deviation of 67. se = enter an integer or decimal number, accurate to at least 3 decimal places (more..)

Explanation:

Step1: Recall the formula for standard error

The formula for the standard error (SE) of the distribution of sample means is \(SE=\frac{\sigma}{\sqrt{n}}\), where \(\sigma\) is the population standard deviation and \(n\) is the sample size.

Step2: Substitute the given values into the formula

Given \(\sigma = 67\) and \(n=800\). Then \(SE=\frac{67}{\sqrt{800}}\).
First, calculate \(\sqrt{800}\approx28.284\).
Then \(SE=\frac{67}{28.284}\approx2.369\).

Answer:

\(2.369\)