Question

#1)  An researcher  wishes to see if the primary way people obtain information is independent of their highest level of education. A survey of 400 high school and college graduates yielded the following information. At the a = 0.05 significance level, test the claim that the way people obtained information is independent of their education level.

                         TV        Newspaper      Other sources

     High school                        163            30                  52

            College                        37             65                  53

   - A clear statement of hypotheses
   - An indication of the test being used
   - Statement of the test statistic and either p-value (or appropriate critical value)
   - Explicit statement of the statistical decision, along with a reason
   - A specific conclusion based on the statistical decision

Answer 1

Ans:

Chi square test for independence:

H0: The way people obtained information is independent of their education level.

Ha:The way people obtained information is not independent of their education level.

	Observed(fo)
	TV	News paper	Others	Total
High school	163	30	52	245
College	37	65	53	155
Total	200	95	105	400
	Expected(fe)
	TV	News paper	Others	Total
High school	122.5	58.1875	64.3125	245
College	77.5	36.8125	40.6875	155
Total	200	95	105	400
	Chi square=(fo-fe)^2/fe
	TV	News paper	Others	Total
High school	13.390	13.655	2.357	29.402
College	21.165	21.583	3.726	46.474
Total	34.554	35.238	6.083	75.875

Test statistic:

Chi square=75.875

df=(2-1)*(3-1)=2

p-value=CHIDIST(75.875,2)=0.0000

As,p-value<0.05,we reject the null hypothesis.

There is sufficient evidence to reject the claim that  the way people obtained information is independent of their education level.