Question

A dice was thrown 60 times with the following results:

Face 1 2 3 4 5 6 Total

Frequency 6 10 8 13 11 12 60

Are the data consistent with the hypothesis that the dice is unbiased?



-

= 15.09 at 1% level for 5 d.f.​

Answer 1

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Answer 2

Answer:

Given: The table with face and frequency

To find: the data consistent with the hypothesis that the dice is unbiased

Solution:

Null hypothesis: die is fair

$\begin{aligned}x^{2} &=\frac{(4-10)^{2}}{10}+\frac{(6-10)^{3}}{10}+\frac{(77-10)^{2}}{10}+\frac{(16-10)^{2}}{10}+\frac{(8-10)^{2}}{10}+\frac{(9-10)^{3}}{10} \\&=14.2, d f=5\end{aligned}$

$p -$value $\approx 2 \%_{0}$, reject the null.

The die 19 is properly biased.

The Chi-Squared $\left(\chi^{2}\right)$ statistic can be used to test the hypothesis that data were generated according to a particular chance model.

$\chi^{2}=\text { sum of } \frac{(\text { observed frequency - expected frequency })^{2}}{\text { expected frequency }}$