All tests generate a complete report of all calculations in the form of a userinfo message.  In order to access these reports when applying tests, specify infolevel[Statistics] := 1 or use the summarize option.

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

$S≔\mathrm{Sample}\left(\mathrm{Rayleigh}\left(7\right)\,100\right)\:$

$\mathrm{evalf}\left(\mathrm{Mean}\left(\mathrm{Rayleigh}\left(7\right)\right)\right)$

$8.773198959$

$\mathrm{evalf}\left(\mathrm{StandardDeviation}\left(\mathrm{Rayleigh}\left(7\right)\right)\right)$

$4.585954642$

$\mathrm{OneSampleZTest}\left(S\,8\,5\right)$

$\mathrm{hypothesis}=\mathrm{false},\mathrm{confidenceinterval}=8.19465579918747..10.1546197837269,\mathrm{distribution}=\mathrm{Normal}\left(0\,1\right),\mathrm{pvalue}=0.0188099792028316,\mathrm{statistic}=2.34927558291438$

$\mathrm{OneSampleTTest}\left(S\,8\right)$

$\mathrm{hypothesis}=\mathrm{false},\mathrm{confidenceinterval}=8.26546145701860..10.0838141258958,\mathrm{distribution}=\mathrm{StudentT}\left(99\right),\mathrm{pvalue}=0.0118640683436966,\mathrm{statistic}=2.56356894641468$

$\mathrm{ShapiroWilkWTest}\left(S\,\mathrm{summarize}=\mathrm{embed}\right)$

$\mathrm{hypothesis}=\mathrm{false},\mathrm{pvalue}=0.00138375156142846,\mathrm{statistic}=0.947243047976463$

$\mathrm{ChiSquareSuitableModelTest}\left(S\,\mathrm{Normal}\left(8.77\,4.59\right)\,\mathrm{level}=0.01\right)$

$\mathrm{hypothesis}=\mathrm{true},\mathrm{criticalvalue}=21.6659943178256,\mathrm{distribution}=\mathrm{ChiSquare}\left(9\right),\mathrm{pvalue}=0.474985626461966,\mathrm{statistic}=8.600000000$

$X≔\mathrm{Matrix}\left(\left[\left[32.\,12.\right]\,\left[14.\,22.\right]\,\left[6.\,9.\right]\right]\right)\:$

$\mathrm{ChiSquareIndependenceTest}\left(X\,\mathrm{level}=0.05\right)$

$\mathrm{hypothesis}=\mathrm{false},\mathrm{criticalvalue}=5.99146454710798,\mathrm{distribution}=\mathrm{ChiSquare}\left(2\right),\mathrm{pvalue}=0.00471928013399603,\mathrm{statistic}=10.71219801$

$\mathrm{ChiSquareIndependenceTest}\left(X\,\mathrm{level}=0.05\,\mathrm{summarize}=\mathrm{true}\right)$

Chi-Square Test for Independence

--------------------------------

Null Hypothesis:
Two attributes within a population are independent of one another

Alt. Hypothesis:
Two attributes within a population are not independent of one another

Dimensions:              3

Total Elements:          95

Distribution:            ChiSquare(2)

Computed Statistic:      10.71219801

Computed p-value:        .00471928013399603

Critical Values:         5.99146454710798

Result: [Rejected]
This statistical test provides evidence that the null hypothesis is false.

$\mathrm{hypothesis}=\mathrm{false},\mathrm{criticalvalue}=5.99146454710798,\mathrm{distribution}=\mathrm{ChiSquare}\left(2\right),\mathrm{pvalue}=0.00471928013399603,\mathrm{statistic}=10.71219801$