A die rolled 60 times yields counts 8, 12, 9, 11, 10, 10. Under H0 that the die is fair, the expected count per face is 10. The chi-square statistic is approximately

Setting Up a Chi-Square Goodness of Fit Test

AP Statistics· difficulty 4/5

H_0

Explanation

χ² = Σ(O-E)²/E = (4+4+1+1+0+0)/10 = 10/10 = 1.0. With df=5, this is far below the critical value (~11.07 at α=0.05) \to fail to reject.

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