Question

Is the distribution of ages of Georgians that purchase a lottery ticket different from the population?...

Is the distribution of ages of Georgians that purchase a lottery ticket different from the population? To answer this, the distribution of ages of all of Georgians from the most recent census is determined. Next, researchers surveyed a random sample of 200 Georgians that purchased a lottery ticket. Age Group 18-34 35-64 65 and over 2010 Georgia Census 35% 51% 14% Lottery Ticket Survey 63 118 19 (a) What are the null and alternative to determine if there is convincing evidence that the age distribution of Georgians that purchase a lottery ticket is different from that of the population? H0: The age distribution of the census and the survey are not independent vs. Ha: The age distribution of the census and the survey are independent. H0: p1 = 0.35, p2 = 0.51, p3 = 0.14 vs. Ha: at least one of the p's is different H0: The age distribution of the census and the survey are independent vs. Ha: The age distribution of the census and the survey are not independent. H0: p1 = 1/3, p2 = 1/3, p3 = 1/3 vs. Ha: at least one of the p's is different (b) How much does the cell 35-64 contribute to the test statistic? (3 decimal places) (c) The test statistic is 6.103. Determine the p-value. (3 decimal places)

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Homework Answers

Answer #1

Solution:
Given:
researchers surveyed a random sample of 200 Georgians that purchased a lottery ticket.

Age Group 2010 Georgia Census Lottery Ticket Survey
18-34 35% 63
35-64 51% 118
65 and Over 14% 19
N = 200

Part (a) What are the null and alternative to determine if there is convincing evidence that the age distribution of Georgians that purchase a lottery ticket is different from that of the population?

H0: p1 = 0.35, p2 = 0.51, p3 = 0.14 vs. Ha: at least one of the p's is different

Part (b) How much does the cell 35-64 contribute to the test statistic?

Where O35-64 = 118

E35-64 = 200 X 0.51 = 102

Thus

Part c) The test statistic is 6.103. Determine the p-value.

df = k - 1= 3- 1 = 2

Use Excel command:

=CHISQ.DIST.RT( x , df )

=CHISQ.DIST.RT( 6.103 , 2)

=0.047

Thus p-value = 0.047

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