Dawnbridge

TI-Nspire CX II field manual for IB Math

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30

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 exp with the expected counts (120/6=20 each).

*Document
RAD
AobsBexpCD=118.20.222.20.320.20.425.20.515.20.A1
2

Still on the Lists & Spreadsheet page, press 4: Statistics4: Stat Tests7: 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 p0.715, so there is insufficient evidence that the die is unfair.

*Document
RAD
BexpCDE=120.Titleχ² GOF220.χ²2.9320.PVal0.7154420.df5.520.CompList{…}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.