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# What is a Confidence Interval?

## What is Confidence Interval?

A confidence interval is a range of parameters that complements the rejection region. For example, a 95% confidence interval contains the set of parameter values where the null hypothesis cannot be rejected when using a 5% test. More generally, a 1 – α confidence interval contains the values that cannot be rejected when using a test size of .

The bounds of a confidence interval depend on the type of alternative used in the test.

## Example of Confidence Interval:

When Ho:μ is tested against the two-sided alternative (e.g. H1:μ is not equal to μo), then the 1 – α, the confidence interval is:

$[ \mu \, -\, C_{\alpha }\, \times \frac{\sigma }{\sqrt{n},\mu }\, +\, C_{\alpha }\, \times \frac{\sigma }{\sqrt{n}} ]$

Where Cα is a critical value for a two-sided test (e.g. if α = 5%, then the Cα = 1.96)

## Why is confidence interval important?

Confidence intervals are critical when generalising data since they show the range of scores that are likely if the survey is repeated. It assists us in determining the level we are confident about the results.

Owais Siddiqui
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