An article about the California lottery gave the following information on the ag

Question

An article about the California lottery gave the following information on the age distribution of adults in California: 35% are between 18 and 34 years old, 51% are between 35 and 64 years old, and 14% are 65 years old or older. The article also gave information on the age distribution of those who purchase lottery tickets. The following table is consistent with the values given in the article. Suppose that the data resulted from a random sample of 200 lottery ticket purchasers. Based on these sample data, is it reasonable to conclude that one or more of these three age groups buys a disproportionate share of lottery tickets? Use a chi-square goodness-of-fit test with = 0.05. (Round your answer to two decimal places.) Age of Purchaser Frequency 18-34 42 35-64 105 65 and over 53 2 = P-value interval p < 0.001 0.001 p < 0.01 0.01 p < 0.05 0.05 p < 0.10 p 0.10 The data strong evidence to conclude that one or more of the three age groups buys a disproportionate share of lottery tickets.

Explanation / Answer

null hypothesis: Ho: all of these three age groups buys a proportionate share of lottery tickets

alternate hypothesis:Ha:  one or more of these three age groups buys a disproportionate share of lottery tickets

here degree of freedom =number of categories -1=3-1=2

appplying chi square goodness of fit test on above data:

for abvoe test stat and 2 degree of freedom p < 0.001

as p value is very low we reject null hypothesis

there is strong evidence to conclude that one or more of the three age groups buys a disproportionate share of lottery tickets.

category Probability O E=total*p =(O-E)^2/E 18-34 0.350 42.000 70.00 11.20 35-64 0.510 105.000 102.00 0.09 65 and over 0.140 53.000 28.00 22.32 1 200 200 33.6097

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