a simple random sample of items resulted in a sample mean of . the population standard deviation is . round your answers to two decimal places.

We thoroughly check each answer to a question to provide you with the most correct answers. Found a mistake? Let us know about it through the REPORT button at the bottom of the page. Ctrl+F (Cmd+F) will help you a lot when searching through such a large set of questions.

A simple random sample of 20 items resulted in a sample mean of 10. The population standard deviation is = 3. Round your answers to two decimal places.

A. What is the standard error of the mean,?

B. At 95% confidence, what is the margin of error?

Answer

0.7906

What is the standard error of the sample mean?

The standard error of the mean is the standard deviation of the sampling distribution of the sample means.

When the population distribution has standard deviation \sigmaσ, then the sampling distribution of the sample mean \overline{x}  x   has standard deviation \sigma_{\overline{x}}=\frac{\sigma}{\sqrt{n}}σ  x   ​  =  n ​   σ ​  .  \sigma_{\overline{x}}=\frac{\sigma}{\sqrt{n}} σ  x   ​  =  n ​   σ ​
We derive the standard error by substituting the known values for \sigmaσ and nn into the formula for \sigma_{\overline{x}}σ 
x 
​
 .  \sigma_{\overline{x}}=\frac{\sigma}{\sqrt{n}}=\dfrac{5}{\sqrt{40}}\approx 0.7906
σ 
x 
​
 = 
n
​ 
σ
​
 = 
40
​ 
5
​
 ≈0.7906

Was this helpful?