HypothesisTesting`
HypothesisTesting`

# MeanDifferenceCI

MeanDifferenceCI[list1,list2]

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

# Details and Options

• 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 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.
• The following options can be given:
•  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

# Examples

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## Basic Examples(1)

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

## Options(3)

### ConfidenceLevel(1)

The 99% confidence interval:

### EqualVariances(1)

A confidence interval assuming equal but unknown variances:

### KnownVariance(1)

A confidence interval assuming known variances:

Wolfram Research (2007), MeanDifferenceCI, Wolfram Language function, https://reference.wolfram.com/language/HypothesisTesting/ref/MeanDifferenceCI.html.

#### Text

Wolfram Research (2007), MeanDifferenceCI, Wolfram Language function, https://reference.wolfram.com/language/HypothesisTesting/ref/MeanDifferenceCI.html.

#### CMS

Wolfram Language. 2007. "MeanDifferenceCI." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/HypothesisTesting/ref/MeanDifferenceCI.html.

#### APA

Wolfram Language. (2007). MeanDifferenceCI. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/HypothesisTesting/ref/MeanDifferenceCI.html

#### BibTeX

@misc{reference.wolfram_2024_meandifferenceci, author="Wolfram Research", title="{MeanDifferenceCI}", year="2007", howpublished="\url{https://reference.wolfram.com/language/HypothesisTesting/ref/MeanDifferenceCI.html}", note=[Accessed: 21-June-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_meandifferenceci, organization={Wolfram Research}, title={MeanDifferenceCI}, year={2007}, url={https://reference.wolfram.com/language/HypothesisTesting/ref/MeanDifferenceCI.html}, note=[Accessed: 21-June-2024 ]}