Question

4. (a) Five unbiased dice were thrown 96 times and the number of times 4, 5 or 6 was 

obtained, is given in the following table: (5) 

 

No. of dice 

showing 4, 

5 or 6 

0 1 2 3 4 5

Frequency 1 10 24 35 18 8

At 5% level of significance test whether this data comes from a binomial distribution. 

You may like to use the following values. 

 [( 10 05. ) 11 07. ,

2

x5 = 05.0( ) 12 59. ,

2

x6 = 05.0( ) 14 07. .]

Answer 1

$\chi^2$ test is a test of goodness of fit of the Binomial distribution. If the calculated value of $\chi^2$ at a specified level of significance, the hypothesis is accepted. Otherwise the hypothesis is rejected.

$\chi^2=\displaystyle\sum_{i=0}^5\frac{(O_i-E_i)^2}{E_i}$

degrees of freedom$=(2-1)(6-1)=5$

Using online calculator (www.mathsisfun.com), we get:

$\chi^2_{0.5}=9.45<11.07$ (table value)

So, the hypothesis that the data comes from a binomial distribution is accepted.