Question

In 600 throws of a six faced dice, odd points appeared 360 times. Would you say that the dice is fair at 5% level of significance? ​

Answer 1

Given:

600 throws of a six faced dice

odd points appeared 360 times

Find the dice is fair at 5% level of significance = ?

$\text { Let us take the hypothesis that the dice is fair. }$

$\text { In a fair dice we would expect } 300 \text { odd points in } 600 \text { throws }$

$\text { S. E. }=\sqrt{n p q}=\sqrt{600 \times \frac{1}{2} \times \frac{1}{2}}$

$S.E.=\sqrt{300\times1\times\frac{1}{2} } \\\\S.E.=\sqrt{150} \\\\S.E.=12.247$

$Z=\frac{\text { Difference }}{\text { S.E. }}\\\\=\frac{360-300}{12.247}\\\\=4.89$

$\text { Since the difference is more than } 1.96 \text { at } 5 \% \text { level of significance, }$

$the\ hypothesis\ is\ rejected.$

Hence we cannot say that the dice is fair at 5% level of significance.