Question

A researcher recorded all digits selected in California's Daily 4 Lottery for the 60 days preceding the time. The frequencies of the digits 0 to 9 are 21, 30, 31, 33, 19, 23, 21, 16, 24, and 22 respectively.

Use a 0.05 significance level to test the claim that the digits are selected in away that they are equally likely.

-What is the critical value (X 2)? [Round to the nearest thousandths place]

-is there sufficient evidence to reject the claim?

Answer 1

Null hypothesis Ho: he frequencies of the digits 0 to 9 are uniform

Alternate hypothesis Ha: he frequencies of the digits 0 to 9 are not uniform.

degree of freedom =categories-1=			9
for 0.05 level and 9 df :crtiical value X2 =			16.9190	from excel: chiinv(0.05,9)
Decision rule: reject Ho if value of test statistic X2>16.919

applying chi square goodness of fit test:

	relative	observed	Expected		Chi square
Category	frequency(p)	Oi	Ei=total*p		R2i=(Oi-Ei)2/Ei
0	0.1000	21	24.00		0.38
1	0.1000	30	24.00		1.50
2	0.1000	31	24.00		2.04
3	0.1000	33	24.00		3.38
4	0.1000	19	24.00		1.04
5	0.1000	23	24.00		0.04
6	0.1000	21	24.00		0.38
7	0.1000	16	24.00		2.67
8	0.1000	24	24.00		0.00
9	0.1000	22	24.00		0.17
total	1.00	240	240		11.58
test statistic X2=		11.583

since test statistic does not falls in rejection region we fail to reject null hypothesis

we do not have have sufficient evidence to reject the claim.