Confidence Intervals are often used and are a great way to not just give a point estimate but to tell where else the point might be. We will focus on confidence intervals based on normal data today.

## z-confidence intervals for the mean

Suppose data with unknown mean but known variance. The confidence interval is then:

where

## t-confidence intervals for the mean

Suppose where the mean and the variance are unknown. The confidence interval for the mean is:

. Where for T~t(n-1) and is the sample variance.

## Chi-Square confidence intervals for the variance

Suppose and both, the mean and the variance are unknown. The confidence interval is:

where for .

## Conservative normal confidence interval

Suppose are i.i.d. Bin(p) distributed. The conservative normal confidence interval is then:

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