Dawnbridge

TI-Nspire CX II field manual for IB Math

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32

χ2 goodness-of-fit test

Maths AI

Run a χ2 goodness-of-fit test on observed and expected counts entered in lists.

Goal

A die is rolled 120 times, landing on each face ​18,  ​22,  ​20,  ​25,  ​15,  ​20​ times. Test at the 5% level whether the die is fair.

1

Open a Lists & Spreadsheet page. Name one column obs with the observed counts and another expec with the expected counts (​120/6=20​ each). The name exp itself is rejected: it already belongs to the exponential function.

*Document
RAD
AobsBexpecCD=1182022220320204252051520A1
2

Still on the Lists & Spreadsheet page, press → 4: Statistics → 4: Stat Tests → 7: χ² GOF. Set the observed and expected lists, Deg of Freedom: 5 (categories minus one), and leave 1st Result Column pointing at the next empty column, moving between fields with .

*Document
RAD
χ²-Goodness of Fit Test
Observed List:obs▶
Expected List:exp▶
Deg of Freedom, df:5▶
1st Result Columnc[]▶
OKCancel
3

Select OK and press . The result labels and values paste straight into the spreadsheet.

Result

​χ2=2.9​ and ​p≈0.715, so there is insufficient evidence that the die is unfair.

*Document
RAD
BexpecCDE=120Titleχ² GOF220χ²2.9320PVal0.7154420df5.520CompList{0.2,0.2,0.,1.25,1.25,0.}B1

Your turn

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

  1. 1

    A spinner with 5 equal sectors is spun 100 times, landing ​23,  ​18,  ​25,  ​15,  ​19​ times on each sector. Test at the 5% level whether the spinner is fair.

  2. 2

    A model predicts expected counts ​20,  ​40,  ​40,  ​20​ over 120 trials. The observed counts are ​26,  ​35,  ​44,  ​15. Test the model at the 5% level.

  3. 3

    A die-like device with 6 equally likely outcomes is used 90 times, giving observed counts ​12,  ​19,  ​15,  ​21,  ​10,  ​13. Test uniformity at the 5% level.