Question

Question 7. A television station wishes to study the relationship between viewership of its 11 p.m. news program and viewer age (18 years or less, 19 to 35, 36 to 54, 55 or older). A sample of 250 television viewers in each age group is randomly selected, and the number who watch the station’s 11 p.m. news is found for each sample. The results are given in the table below.

		Age Group
Watch 11 p.m. News?	18 or less	19 to 35	36 to 54	55 or Older	Total
Yes	37	48	67	84	236
No	213	202	183	166	764
Total	250	250	250	250	1,000

(a) Let p₁, p₂, p₃, and p₄ be the proportions of all viewers in each age group who watch the station’s 11 p.m. news. If these proportions are equal, then whether a viewer watches the station’s 11 p.m. news is independent of the viewer’s age group. Therefore, we can test the null hypothesis H₀ that p₁, p₂, p₃, and p₄ are equal by carrying out a chi-square test for independence. Perform this test by setting α = .05. (Round your answer to 3 decimal places.)

X^2 = ____

Answer 1

a)

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	<18	19-35	36-54	>55	Total
	Yes	59.00	59.00	59.00	59.00	236
	No	191.00	191.00	191.00	191.00	764
	total	250	250	250	250	1000
chi square    χ2	=(Oi-Ei)2/Ei	<18	19-35	36-54	>55	Total
	Yes	8.203	2.051	1.085	10.593	21.9322
	No	2.534	0.634	0.335	3.272	6.7749
	total	10.7374	2.6844	1.4198	13.8655	28.7071
test statistic X2 =		28.707