Chi-square goodness of fit

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Problem

A die is rolled $60$ times, producing face counts $(8,9,10,11,12,10)$ . Test the null hypothesis that the die is fair using a chi-square goodness-of-fit test. Compute the statistic and degrees of freedom, and decide at $5\%$ using critical value $11.07$ .

Reveal answer or reference solution

Under fairness each expected count is $10$ . The statistic is

\chi^2=\sum_{i=1}^6\frac{(O_i-10)^2}{10} =\frac{4+1+0+1+4+0}{10}=1

No parameter was fitted, so the degrees of freedom are $6-1=5$ . Since $1<11.07$ , do not reject the fair-die null at the $5\%$ level.

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Chi-square goodness of fit

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