Step 1: The University of Chicago\'s General Social Survey (GSS) is the nation\'

Question

Step 1: The University of Chicago's General Social Survey (GSS) is the nation's most important social science sample survey. The GSS asked a random sample of adults their opinion about whether astrology is very or sort of scientific or not at all scientific. Is belief that astrology is scientific related to amount of higher education? Here is a two-way table of counts for people in the sample who had three levels of higher education degrees:

Is the observed association between these variables statistically significant? Add the row and column totals to the two-way table shown above and find the expected cell counts. Which observed counts differ most from the expected counts?

b and e

Step 2:
Find the chi-square statistic. Give its value to two decimal places.

Step 3:
What are the degrees of freedom?

Step 4:
Use Table 24.1 (page 565) to say how significant the chi-square test is.

P < 0.01

Junior College Bachelor Master Not at all scientific a b c Very or sortof scientific d e f
Opinion Not at all scientific Very or sort of scientific Degree Held Junior college Bachelor Graduate 198 87 57 43 28

Explanation / Answer

applying chi square goodness of test:

from above as a and d has highest value of chi square ;

hence

Which observed counts differ most from the expected counts? ---a and d

step 2: chi stat =7.24

step 3: degree of freedom =(rows-1)*(column-1)=(2-1)*(3-1)=2

step 4: 0.025<p<0.05

step 5: There is a relationship between education and accepting astrology as science. Specifically, those with junior college degrees are most likely to accept astrology as science, and those with master's degrees are least likely.

Observed O Junior College Bachelor Master Total not at all 87 198 111 396 very or sort of 43 57 28 128 Total 130 255 139 524 Expected E=rowtotal*column total/grand total Junior College Bachelor Master Total not at all 98.244 192.710 105.046 396 very or sort of 31.756 62.290 33.954 128 Total 130 255 139 524 chi square =(O-E)^2/E Junior College Bachelor Master Total not at all 1.287 0.1452 0.3375 1.770 very or sort of 3.981 0.449 1.044 5.475 Total 5.268 0.594 1.382 7.244

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