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Hypothesis Testing Package Symbol

MeanDifferenceCI

MeanDifferenceCI[list₁, list₂]
gives a confidence interval for the difference between the population means estimated from list₁ and list₂.

To use MeanDifferenceCI, you first need to load the Hypothesis Testing Package using Needs["HypothesisTesting`"].

MeanDifferenceCI[list₁, list₂] gives a confidence interval {min, max} centered at Mean[list₁]-Mean[list₂].

MeanDifferenceCI is based on a normal distribution if the population variances are assumed known.

If the variances for the two populations are assumed equal and unknown, the interval is based on Student's t distribution with Length[list₁]+Length[list₂]-2 degrees of freedom.

If the population variances are not assumed known and not assumed equal, Welch's approximation for the degrees of freedom is used.

ConfidenceLevel	0.95	probability associated with a confidence interval
EqualVariances	False	whether the unknown population variances are assumed equal
KnownVariance	None	list of variances of each population

The 95% confidence interval for the difference in two population means:

Needs["HypothesisTesting`"]

The 95% confidence interval for the difference in two population means:

The 99% confidence interval:

A confidence interval assuming equal but unknown variances:

A confidence interval assuming known variances: