3. Tests of independence Aa Aa A New York Times/CBS News poll conducted in Octob

Question

3. Tests of independence Aa Aa A New York Times/CBS News poll conducted in October 2007 surveyed American consumers on their views of Chinese products. Consumers were asked whether they noticed the country of origin of their purchases. They were also asked to rate the overall quality of manufactured goods produced in China The following two-way table summarizes the responses to the two survey questions Quality Rating Very Good or Don't Know/Not Poor Fair Good Excellent Applicable Total Notice Country of 218 Origin Don't Notice 346 255 82 910 41 125 48 21 346 Total 259 457 380 130 1,256 The following questions walk you through the steps of a test of the null hypothesis that a consumer's quality rating of Chinese goods is independent of his awareness of country of origin Fill in the three missing values in the two-way table

Explanation / Answer

notice country of origin/fair category = 457*910/1256 = 331.1067

contribution to test statistic = (346-331.1066)^2/331.1067 = 0.669907

test statistic =0.6699 + 57.838 = 58.5079

df = (r-1)9c-1) = (2-1)(5-1) = 4

critical value = 7.78

since TS > critical value

we reject the null hypothesis

for your reference complete excel file is below

Please rate my solution

c1 c2 c3 c4 c5 sum r1 218 346 255 82 9 910 r2 41 111 125 48 21 346 sum 259 457 380 130 30 1256 Eij 1 2 3 4 5 expected 1 187.6513 331.1067 275.3185 94.1879 21.73567 2 71.34873 125.8933 104.6815 35.8121 8.264331 0i 218 346 255 82 9 41 111 125 48 21 Ei 187.6513 331.1067 275.3185 94.1879 21.73567 71.34873 125.8933 104.6815 35.8121 8.264331 sum (Oi-Ei)^2/Ei 4.908281 0.669907 1.499501 1.577112 7.462262 12.90906 1.761895 3.943774 4.147896 19.62618 58.50587

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