Q 8.60 - Elementary Statistics

Question

State True or False. Give Reasons for your answers.

The confidence level can be determined if you know only the margin of error, population standard deviation, and sample size.

Step-by-Step Solution

Answer

The given statement is True.

Step 1: Given Information

Margin of error, population standard deviation, and sample size is known to us.

Step 2: Explanation

We know that

Confidence level, $\left(z_{\frac{a}{2}}\right)=E\left(\frac{\sqrt{n}}{\sigma }\right)$

and

Margin of Error,$E=z_{\frac{a}{2}}\left(\frac{\sigma }{\sqrt{n}}\right)$

Hence, confidence level can be calculated if know only the margin of error, population standard deviation and the sample size.

Hence, the given statement is True.