Q 8.122. - Elementary Statistics

Question

For the one-mean $t-$interval procedure, express the formula for the endpoints of a confidence interval in the form.

Step-by-Step Solution

Answer

Confidence interval $=\overline{x}\pm t_{\frac{a}{2}}\left(\frac{s}{\sqrt{n}}\right)$

Step 1: Concept

Formula used: Margin of error $E=t_{\frac{a}{2}}\left(\frac{s}{\sqrt{n}}\right)$

Step 2: Explanation

In the form, provide the formula for a confidence interval's endpoints.

Point estimate: 

The population mean $\left(\mu \right)$ is estimated using the sample mean $\left(\overline{x}\right)$

The error margin is:

A margin of error is half the length of the confidence interval. The following is the margin of error formula: $E=t_{\frac{a}{2}}\left(\frac{s}{\sqrt{n}}\right)$

Step 3: Explanation

The form of a confidence interval's endpoints is, 

Confidence interval $=$ Point estimates $\pm$ the margin of error $\left(E\right)$

Confidence interval $=\overline{x}\pm t_{\frac{a}{2}}\left(\frac{s}{\sqrt{n}}\right)$