Question

Each of the digits in a raffle is thought to have the same chance of occurrence. The table shows the frequency of each digit for consecutive drawings in a California lottery. Perform the chi-square test to see if you reject the hypothesis at the 0.02 significance level that the digits are from a uniform population.

Digit	Frequency	Digit	Frequency
0	41	5	35
1	40	6	37
2	41	7	32
3	31	8	33
4	38	9	32

State the decision rule. Use 0.02 significance level. (Round your answer to 3 decimal places.)

H₀: The digits are uniformly distributed.

H₁: The digits are not uniformly distributed.

1) Reject H0 if chi-square > _____

2) Compute the value of chi-square

Answer 1

1)

Reject H0 if chi-square >19.679

2)applying chi square test:

	relative	observed	Expected	residual	Chi square
category	frequency	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
0	0.1000	41	36.00	0.83	0.694
1	0.1000	40	36.00	0.67	0.444
2	0.1000	41	36.00	0.83	0.694
3	0.1000	31	36.00	-0.83	0.694
4	0.1000	38	36.00	0.33	0.111
5	0.1000	35	36.00	-0.17	0.028
6	0.1000	37	36.00	0.17	0.028
7	0.1000	32	36.00	-0.67	0.444
8	0.1000	33	36.00	-0.50	0.250
9	0.1000	32	36.00	-0.67	0.444
total	1.000	360	360		3.833

value of chi-square =3.833