Question

A die is rolled 264 times with the following results : No. that comes up : 1 2 3 4 5 6 Frequency : 40 32 28 50 54 60
Test, if the die. is unbiased at 5% level of significance. (Given that x 0.05 (5) = 11.07)

Answer 1

Answer:

I am not in this std you can also ask questions of low levels plz

Answer 2

Concept

The Chi- squared$(\chi ^2)$ test can be used to test the hypothesis that the data were generated according to a particular chance model.

Given

No. appeared on the die    $1$           $2$         $3$           $4$         $5$          $6$

Frequency                           $40$        $32$        $28$         $50$       $54$         $60$      

To find

If the dies is unbiased at $5\%$ level of significance

Solution

• Null hypothesis: The die is unbiased
• On the basis of hypthesis each number is expected to turn up $\dfrac{264}{6} =44$ times

$\chi^2=\sum_{x=1}^{n} \left [ \dfrac{(O_x-E_x)^2}{E_x} \right ]$

Observed($(O_x)$           Expected($(E_x)$            $(O_x-E_x)^2$         $\dfrac{(O_x-E_x)^2}{E_x}$

     $40$                                  $44$                                 $16$                      $0.36$

     $32$                                  $44$                                 $144$                     $3.27$

     $28$                                  $44$                                 $256$                     $5.82$

     $50$                                  $44$                                  $36$                      $0.82$

     $54$                                  $44$                                 $100$                     $2.27$

     $60$                                  $44$                                 $256$                     $5.82$

$\chi^2=0.36+3.27+5.82+0.82+2.27+5.82=18.36$

Number of degrees of freedom$=n-1=6-1=5$

Calculated $\chi^2$ value$=18.36$

Tabulated value$=11.07$(at $5\%$ level of significance with $5$ degrees of freedom)

Calculated value $>$ Tabulated value

Reject the null hypothesis. Die is probably biased.

As a result, Die is probably biased.