Question

In a three-digit lottery, each of the three digits is supposed to have the same probability of occurrence (counting initial blanks as zeros, e.g., 32 is treated as 032). The table shows the frequency of occurrence of each digit for 90 consecutive daily three-digit drawings.
    

Digit	Frequency
0		26
1		23
2		29
3		38
4		30
5		26
6		26
7		20
8		27
9		25
Total		270

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

Test statistic
d.f.
p-value

(b) Choose the correct answer by drawing a bar chart for the above data.

• The graph will reveal that 7 occurs least frequently.

• The graph will reveal that 8 occurs least frequently.

• The graph will reveal that 3 occurs least frequently.

• The graph will reveal that 4 occurs least frequently.

(c) At α = .10, we cannot reject the hypothesis that the digits are from a uniform population.

• True

• False

Answer 1

Chi square table
Digit	Frequency	E	O-E	(O-E)2/E
0	26	27	-1	0.037037
1	23	27	-4	0.592593
2	29	27	2	0.148148
3	38	27	11	4.481481
4	30	27	3	0.333333
5	26	27	-1	0.037037
6	26	27	-1	0.037037
7	20	27	-7	1.814815
8	27	27	0	0
9	25	27	-2	0.148148
Total	270	270	0	7.62963
expected count=	270/10 =27
H0:	Digits are distributed  uniformly
H1:	Digits are not distributed  uniformly
(a)The chi-square test statistic =	7.63
degrees of freedom =	9
p-value =	0 .5718

(b) The graph will reveal that 8 occurs least frequently.

(c) At α = .10, we cannot reject the hypothesis that the digits are from a uniform population.

• True since p-value > 0.10