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 α = 0.05. (Round your answer to two decimal places.)

Age of Purchaser	Frequency
18-34	40
35-64	100
65 and over	60

χ² =  

P-value interval

p < 0.0010.001 ≤ p < 0.01    0.01 ≤ p < 0.050.05 ≤ p < 0.10p ≥ 0.10

Answer 1

following table is obtained:

Categories	Observed	Expected	(fo-fe)2/fe
Category 1	40	200*0.35=70	(40-70)2/70 = 12.857
Category 2	100	200*0.51=102	(100-102)2/102 = 0.039
Category 3	60	200*0.14=28	(60-28)2/28 = 36.571
Sum =	200	200	49.468

from the above calculated table

χ² =  49.47

with χ² =  49.47 , df = 2

we get p value = 0.00001

Answer : p < 0.001