Dawnbridge

TI-84 Plus CE 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

Enter the observed table as matrix [A]: press to open MATRIX, move to EDIT, choose 1:[A], set the dimensions to 2 x 3, and fill in the counts.

NORMALFLOATAUTOREALRADIANMP
MATRIX[A] 2 x3
301515202515
2

Press , move right to TESTS, and scroll down to C: χ²-Test. Leave Observed: [A] and Expected: [B]: the calculator computes the expected counts into [B] for you.

NORMALFLOATAUTOREALRADIANMP
χ²-Test
Observed:[A]
Expected:[B]
Color:BLUE
CalculateDraw
3

Move down to Calculate 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.

NORMALFLOATAUTOREALRADIANMP
χ²-Test
χ²=4.5
p=0.1053992246
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.