12.16 A random sample of 1000 registered voters in a certain county is selected, and each voter is categorized with respect to both educational level (four categories) and preferred candidate in an upcoming election for county supervisor (five possibilities). The hypothesis of interest is that educational level and preferred candidate are inde- pendent factors.

a.    If X 2 = 7.2, what would you conclude at significance

level .10?

b.    If there were only four candidates vying for election, what would you conclude if X 2 = 14.5 and a = .05?

 

Responses consistent with percentages given in the article for the samples from Italy, Spain, France, the United States, and South Korea are summarized in the accompanying table. Based on these data, is it reasonable to conclude that the response proportions are not the same for all five coun- tries? Use a .01 significance level to test the appropriate hypotheses.

 

Response

 

Some-                    Not

 

Italy 600 140 140 90 30 Spain 540 160 140 70 90 France 400 250 200 120 30 United States 360 230 270 110 30 South Korea 100 330 470 60 40

Country                 Never    Rarely   times       Often    Sure