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Casio fx-CG50 field manual for IB Math

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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

From the MAIN MENU, open Statistics, then press (TEST), (CHI), and (2WAY).

2

With the cursor on Observed, press (▶MAT) to jump to the matrix editor. With Mat A highlighted press (DIM) and enter 2 then 3, then fill in the observed counts, pressing after each value. Press to return to the test form.

RadNorm2
d/cReal
A12313015152202515
ROW-OPROWCOLUMNEDIT
3

Leave Observed: Mat A and Expected: Mat B: the calculator computes the expected counts into Mat B for you.

RadNorm2
d/cReal
χ² Test
Observed:Mat A
Expected:Mat B
Save Res:None
GphColor:Blue
Execute
Mat▶MAT
4

Move down to Execute and press .

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.

RadNorm2
d/cReal
χ² Test
χ²=4.5
p=0.10539922
df=2

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.