Question

14. A die is thrown 300 times with the following results:

No turned up	1	2	3	4	5	6
Frequency	38	46	56	34	64	62

Is the die biased?

Answers should be in word version Format Please

Answer 1

Here hypothesis is

H₀ : The die is not biased.

H_a : The die is biased.

Here the expected number of frequency for die roll = 300/6 = 50

here we will employ chi-square statistic

=

No. Turned Up	Frequency	Expected Frequency	Chi-square value
1	38	50	2.88
2	46	50	0.32
3	56	50	0.72
4	34	50	5.12
5	64	50	3.92
6	62	50	2.88
Sum	300	300	15.84

= 15.84

Here we will assume significane value = 0.05,

so here degree of freedom = dF = n-1 = 6 -1 = 5

Critical value = CHIINV(0.05,5) = 11.07

so here > _critical so we would reject the null hypothesis and conclude that the die is biased.