Question

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

Short answer

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

Step-by-step solution

Concept

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

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:$E=t_{\frac{a}{2}}\left(\frac{s}{\sqrt{n}}\right)$

Explanation

The form of a confidence interval's endpoints is,

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

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