The California Daily 3 lottery game is identical to the Pennsylvania Daily Numbe

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.

Explanation / Answer

a)null hypothesis: all digits occurs with equal frequency or proportion of each digit pi=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:

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

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

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