Casio fx-CG50 field manual for IB Math
χ2 goodness-of-fit test
Run a χ2 goodness-of-fit test on observed and expected counts entered in lists.
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.
From the MAIN MENU, open Statistics. Enter the observed counts in List 1 and the expected counts (120/6=20 each) in List 2, pressing after each value.
Press (TEST), then (CHI), then (GOF). Set Observed: List1, Expected: List2, and df: 5 (categories minus one); CNTRB is the list the calculator writes each category's contribution into.
Press (CALC).
χ2=2.9 and p≈0.715, so there is insufficient evidence that the die is unfair.
Your turn
Work each one on your calculator, then check the answer.
- 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
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
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.