Question

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  = 0.05 significance level, test the claim that the way people obtained information is independent of their education level.

- 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.

	TV	Newspaper	Other
HighsSchool	163	30	52
College	37	65	53

Answer 1

Null hypothesis : Ho : The way people obtained information is independent of their education level. (or way people obtained information and their education level are not associated)

  

Alternative Hypothesis : Ha: The way people obtained information is dependent of their education level.(or way people obtained information and their education level are associated)

Chi-square test for Association

Test Statistic

O : Observed Frequency

E: Expected Frequency

Given: Observed frequency : O

Observed Counts/Frequency	TV	Newspaper	Other	Row Total
HighsSchool	163	30	52	245
College	37	65	53	155
Column Total	200	95	105	400

E: Expected Count/Frequency	TV	Newspaper	Other
HighsSchool	(245*200) / 400	(245*95) / 400	(245*105) / 400
College	(155*200) / 400	(155*95) / 400	(155*105) / 400

E: Expected Count/Frequency	TV	Newspaper	Other
HighsSchool	122.5000	58.1875	64.3125
College	77.5000	36.8125	40.6875

O	E	O-E	(O-E)2
163	122.5000	40.5000	1640.2500	13.3898
30	58.1875	-28.1875	794.5352	13.6547
52	64.3125	-12.3125	151.5977	2.3572
37	77.5000	-40.5000	1640.2500	21.1645
65	36.8125	28.1875	794.5352	21.5833
53	40.6875	12.3125	151.5977	3.7259
			Total	75.8755

Test Statistic

Value of the test statistic = 75.8755

Degrees of freedom = (Number of rows - 1) x (Number of columns - 1) =(2-1)x(3-1)=1x2=2

For 2 degrees of freedom,

p-value = 0.0000

Level of significance : = 0.05;

Critical value of : for 2 degrees of freedom = 5.991

Statistical decision:

As p-value:0.0000 < Level of significance : : 0.05; Reject the null hypothesis.

As Value of the test statistic : 78.8755 > Critical value : 5.991 ; Reject the null hypothesis.

Specific conclusion :

At 0.05 significance level there is sufficient evidence to conclude that  the way people obtained information is dependent of their education level.