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	113
65 and over	47

χ² =

P-value interval

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

The data  ---Select--- provide do not provide strong evidence to conclude that one or more of the three age groups buys a disproportionate share of lottery tickets.

Answer 1

Null hypothesis : Ho :All the three age groups buys a proportionate share of lottery tickets

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

Given,

Age distribution of adults :

18-34 years old - 35%

35-64 years old - 51%

65 and over years old - 14%

Total number of lottery ticket purchasers =200

Test Statistic

Age of purchaser	Observed frequecny	% Adults in the California	Expected Frequency
18-34	40	35%	35% of 200 =70
35-64	113	51%	51% of 200 =102
65 and over	47	14%	14% of 200 =28
Total	200

= 26.94

Degrees of freedom = Number age groups -1 =3-1=2

For 2 degrees of freedom and = 26.94 ; p-value < 0.001 (as for 2 df = 13.82)

P-value interval

p < 0.001

As p-value is less than : 0.05 ; reject the null hypotehsis.

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