Question

The California Daily 3 lottery game is identical to the Pennsylvania Daily Number game describe in Example 15.15. The following table contains the observed distribution of all digits drawn in the California Daily 3 on the 200 days between May 14th, 2000, and November 29, 2000. Three digits are drawn each day, so the sample size is n = 600 for this table. (SHOW YOUR WORK)

table.
Digit    0   1   2   3 4   5 6   7   8 9
Count 49 61 64 62 50 64 59 65 63 63
(a) (3 points) State the null and alternative hypotheses using words and proper statistical notation.
(b) (1 point) Find the expected counts for each number, assuming each number is equally likely.
(c) (3 points) Calculate the chi-square goodness-of-fit statistic. Round your test statistic to two decimal places.
(d) (1 point) What are the degrees of freedom?
(e) (2 points) Find the p-value (Excel) and p-value range (Table).
(f) (2 points) Form a conclusion using the = 0:05 level of significance, and write it in the context of the
situation.

Answer 1

a)null hypothesis: all digits occurs with equal frequency or proportion of each digit p_i=1/10

alternate hypothesis:Ha: at least one digit occurs with differemt frequency or not all pi are equal to 1/10

b)

expected counts =np=600/10=60

c)

applyinf chi square test:

		observed	Expected		Chi square
category	Probability(p)	Oi	Ei=total*p		R2i=(Oi-Ei)2/Ei
0	0.100	49.000	60.000		2.017
1	0.100	61.000	60.000		0.017
2	0.100	64.000	60.000		0.267
3	0.100	62.000	60.000		0.067
4	0.100	50.000	60.000		1.667
5	0.100	64.000	60.000		0.267
6	0.100	59.000	60.000		0.017
7	0.100	65.000	60.000		0.417
8	0.100	63.000	60.000		0.150
9	0.100	63.000	60.000		0.150
total	1.000	600	600		5.033

test statistic =5.03

d)

degree of freedom=categories-1=9

e)

p value =0.8314

range p value >0.1

f)

as p value is greaterr than 0.05 level we can not reject null hypothesis

we do not have sufficient evidence to conclude that at least one digit occurs with differemt frequency or not all pi are equal to 1/10