Is the die fair?

Topic: Chi-squared tests · more questions on this topic
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A die is rolled 120 times, giving faces 1 to 6 with frequencies 14, 22, 16, 25, 19 and 24. Test whether the die is fair at level 0.05. Use \chi^2_{5;0.95}=11.07.

Worked answer (click to show)

Under H_0 each face has probability 1/6, so each expected count is 120/6=20. Then

T=\frac{(14-20)^2+(22-20)^2+(16-20)^2+(25-20)^2+(19-20)^2+(24-20)^2}{20}=\frac{36+4+16+25+1+16}{20}=4.90,

on 6-1=5 degrees of freedom. Since 4.90<11.07, the test does not reject fairness; the p-value is 0.43.