Question

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	45	51	67	84	247
No	205	199	183	166	753
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.)

χ2χ2 =            

so (Click to select)Do not rejectReject H₀: independence

(b) Compute a 95 percent confidence interval for the difference between p₁ and p₄. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.)

95% CI: [  , ]

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	61.7500	61.7500	61.7500	61.7500	247.00
	no	188.2500	188.2500	188.2500	188.2500	753.00
	total	250.00	250.00	250.00	250.00	1000.00
chi square    χ2	=(Oi-Ei)2/Ei	<18	19-35	36-54	>55	Total
	yes	4.544	1.871	0.446	8.017	14.8785
	no	1.490	0.614	0.146	2.630	4.8805
	total	6.0339	2.4853	0.5928	10.6470	19.759
test statistic X2 =		19.759

Reject H₀: independence

b)

estimated difference in proportion   =p̂1-p̂2   =			-0.1560
std error Se =√(p̂1*(1-p̂1)/n1+p̂2*(1-p̂2)/n2) =			0.0385
for 95 % CI value of z=		1.960
margin of error E=z*std error =		0.0755
lower bound=(p̂1-p̂2)-E=		-0.2315
Upper bound=(p̂1-p̂2)+E=		-0.0805
from above 95% confidence interval for difference in population proportion =(-0.231,-0.081)