Question

5 XVI. (Hint: See 8.1 and recall the work we did in class for this section.) a. Test the fairness of the die with a = = 0.10 Numbers: 2 3 4 5 6 Obs: 43 58 42 39 57 61 b. Can you conclude that the die is fair? Why or why not.

Answer 1

Answer:-

Given that:-

a)

observed frequency ,O	expected proportion	expected frequency, E	(O-E)		(O-E)^{2}/E
43	0.167	50.00	-7.00		0.980
58	0.167	50.00	8.00		1.280
42	0.167	50.00	-8.00		1.280
39	0.167	50.00	-11.00		2.420
57	0.167	50.00	7.00		0.980
61	0.167	50.00	11.00		2.420

chi square test statistic ,$X^{2}=\sum (O-E)^{2}/E=9.360$

level of siginificance ,

a = 0.1

Degree of freedom =k-1=6-1=5

b)P value = 0.0955 [excel function=chisq.dist.rt(test-stat,df)]

Decision : P value <$\alpha,$ Reject

он

DIE IS NOT FAIR