Confidence Intervals
( $σ$ unknown)

To find a confidence interval when the population standard deviation is unknown one uses the formula:

$\overset{―}{x} - t_{α} \cdot (\frac{s}{\sqrt{n}}) < μ < \overset{―}{x} + t_{α} \cdot (\frac{s}{\sqrt{n}})$

The degrees of freedom are $n - 1$ .

As before $α$ is the percent you want the confidence level to be (for example 90%). To find the correct $t$ -value one looks for (\alpha\) at the bottom of the $t$ -table, then follow up to get the $t$ -value for two-tails!

Just like before there are some needed assumptions.

Assumptions for finding confidence interval for a mean when (\sigma\) is unknown.

The sample is a random sample.
Either $n \geq 30$ or the population is normally distributed when $n < 30$ .

Confidence Intervals
( $σ$ unknown)

Confidence Intervals(σ unknown)

Confidence Intervals(σ unknown)

Confidence Intervals
( $σ$ unknown)

Confidence Intervals
( $σ$ unknown)