Dawnbridge

TI-Nspire CX II field manual for IB Math

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31

χ2 test of independence

Maths AI

Run a χ2 test of independence on a contingency table entered as a matrix.

Goal

120 students are classified by year group and preferred subject. Test at the 5% level whether preference is independent of year group, given the observed table ​[3020​1525​1515​].

1

Store the observed table as a matrix: on the Scratchpad calculator, type obs:=, then press → 7: Matrix & Vector → 1: Create → 1: Matrix. A dialog asks for the number of rows and columns — type ( moves between the fields). This drops an empty 2 x 3 template into the entry line; fill in the six counts (moving between cells with ) and press .

Scratchpad
RAD
obs:=[3020​1525​1515​]
[3020​1525​1515​]
2

Press → 6: Statistics → 7: Stat Tests → 8: χ² 2-way Test and set Observed Matrix to obs.

Scratchpad
RAD
χ²-2-way Test
Observed Matrix:obs▶
OKCancel
3

Select OK and press . The test results (including the expected-counts matrix) land on the Scratchpad.

Result

​χ2=4.5​ with ​df=2​ and ​p≈0.105, so there is insufficient evidence of an association: preference appears independent of year group.

Scratchpad
RAD
obs:=[30.20.​15.25.​15.15.​]
[30.20.​15.25.​15.15.​]
χ22wayobs:stat.results
⎣⎢⎢⎢⎢⎢⎢⎡​”Title””χ²””PVal””df””ExpMatrix””CompMatrix”​”χ² 2-way Test”4.50.1053992.”[…]””[…]”​⎦⎥⎥⎥⎥⎥⎥⎤​

Your turn

Work each one on your calculator, then check the answer.

  1. 1

    100 students are classified by gender and by whether they passed: observed table ​[3525​1525​]. Test independence at the 5% level.

  2. 2

    165 customers are classified by age band and preferred product: observed table ​⎣⎡​202515​302010​101520​⎦⎤​. Test independence at the 5% level.

  3. 3

    120 students are classified by year group and preferred sport: observed table ​[1827​2213​2020​]. Test independence at the 5% level.