Question

A variable of a population has a normal distribution. Suppose that you want to find a confidence interval for the population mean.

a. If you know the population standard deviation, which procedure would you use?

b. If you do not know the population standard deviation, which procedure would you use?

Short answer

Part (a) We may use the$Z-$interval approach to get the confidence interval for the population mean$\mu$if we know the population standard deviation, $\sigma$

Part (b) The $t-$interval approach will be used to establish the confidence interval of $\mu$ if the population $s.d.$ and $\sigma$ are unknown.

Step-by-step solution

Part (a) Step 1: Given information

A variable of a population has a normal distribution.

Part (a) Step 2: Explanation

If we know the population $s.d.$, $\sigma$, we may use the $Z-$interval approach to obtain the confidence interval for the population mean $\mu$

Part (b) Step 1: Explanation

If the population $s.d.$ and $\sigma$ are unknown, the $t-$interval approach will be used to determine the confidence interval of $\mu$