Question

In a four-digit lottery, each of the four digits is supposed to have the same probability of occurrence. The table shows the frequency of occurrence of each digit for 87 consecutive daily four-digit drawings.

Digit	Frequency
0		37
1		40
2		31
3		43
4		34
5		31
6		37
7		29
8		30
9		36
Total		348

(b) Calculate the chi-square test statistic, degrees of freedom, and the p-value. (Round your test statistic value to 2 decimal places and the p-value to 4 decimal places.)

Test statistic
d.f.
p-value

(c) Find the critical value of the chi-square for α = .01. (Round your answer to 2 decimal places.)

Critical value:   

Answer 1

observed frequencey, O	expected proportion	expected frequency,E	(O-E)		(O-E)²/E
37	0.100	34.80	2.20		0.139
40	0.100	34.80	5.20		0.777
31	0.100	34.80	-3.80		0.415
43	0.100	34.80	8.20		1.932
34	0.100	34.80	-0.80		0.018
31	0.100	34.800	-3.80		0.415
37	0.100	34.800	2.20		0.139
29	0.100	34.800	-5.80		0.967
30	0.100	34.800	-4.80		0.662
36	0.100	34.800	1.20		0.041

b)

chi square test statistic,X² = Σ(O-E)²/E =   5.51   
                  
  
Degree of freedom=k-1=   10   -   1   =   9
                  
P value =   0.7882   [ excel function: =chisq.dist.rt(test-stat,df) ]          

c)

Critical value =    21.67

Decision: P value >α ,     Do not reject Ho