Student:-Statistics subpackage contains commands that are used for hypothesis tests for basic academic statistics. Each of the hypothesis tests returns all the important information of the test, including the final conclusion as well as the core values used in the computing process.

Hypothesis tests available in Student:-Statistics are:

The command TestsGuide is designed to guide users to use the appropriate test on particular arguments. In addition, TestsGuide is also designed with visualization of some of the hypothesis tests to give a better demonstration of the returned conclusion; explanations and instructions of use of all the hypothesis tests are also available within this command.

$\mathrm{with}\left(\mathrm{Student}:-\mathrm{Statistics}\right)\:$

$A≔\mathrm{BetaRandomVariable}\left(2\,4\right)\:$

$S≔\mathrm{Sample}\left(A\,1000\right)\:$

$\mathrm{Mean}\left(A\right)$

$\frac{1}{3}$

$\mathrm{OneSampleTTest}\left(S\,\frac{1}{2}\right)$

Standard T-Test on One Sample
-----------------------------
Null Hypothesis:
Sample drawn from population with mean 0.5
Alt. Hypothesis:
Sample drawn from population with mean not equal to 0.5
 
Sample Size:             1000
Sample Mean:             0.330871
Sample Standard Dev.:    0.172759
Distribution:            StudentT(999)
Computed Statistic:      -30.9583453553696
Computed p-value:        4.40097527534518e-148
Confidence Interval:     .320150504664501 .. .341591498494785
                         (population mean)
 
Result: [Rejected]
This statistical test provides evidence that the null hypothesis is false.

$\left[\mathrm{hypothesis}=\mathrm{false}\,\mathrm{confidenceinterval}=0.320150504664501..0.341591498494785\,\mathrm{distribution}=\mathrm{StudentT}\left(999\right)\,\mathrm{pvalue}=4.40097527534518\times {10}^{\mathrm{-148}}\,\mathrm{statistic}=\mathrm{-30.9583453553696}\right]$

$\mathrm{ChiSquareSuitableModelTest}\left(S\,A\right)$

Chi-Square Test for Suitable Probability Model
----------------------------------------------
Null Hypothesis:
Sample was drawn from specified probability distribution
Alt. Hypothesis:
Sample was not drawn from specified probability distribution
 
Bins:                    32
Degrees of Freedom:      31
Distribution:            ChiSquare(31)
Computed Statistic:      36.60800000
Computed p-value:        .224557190878386
Critical Values:         44.9853428040743
 
Result: [Accepted]
This statistical test does not provide enough evidence to conclude that the null hypothesis is false.

$\left[\mathrm{hypothesis}=\mathrm{true}\,\mathrm{criticalvalue}=44.9853428040742\,\mathrm{distribution}=\mathrm{ChiSquare}\left(31\right)\,\mathrm{pvalue}=0.224557190878386\,\mathrm{statistic}=36.60800000\right]$