Dawnbridge

TI-84 Plus CE 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 the list editor with → 1: Edit. Enter the observed counts in L1 and the expected counts (​120/6=20​ each) in L2.

NORMALFLOATAUTOREALRADIANMP
L1L2L3L4L51820------------------22202020252015202020------------
2

Press , move right to TESTS, and scroll down to D: χ²GOF-Test. Set Observed: L1 (type L1 with ), Expected: L2 (type L2 with ), and df: 5 (categories minus one).

NORMALFLOATAUTOREALRADIANMP
χ²GOF-Test
Observed:L1
Expected:L2
df:5
Color:BLUE
CalculateDraw
3

Move down to Calculate and press .

Result

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

NORMALFLOATAUTOREALRADIANMP
χ²GOF-Test
χ²=2.9
p=0.7153995143
df=5
CNTRB={0.2 0.2 0 1.25 1.25 0}

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.