Question

In the 2008GSS, among the American Indian respondents, 4 say they are very happy, 15 say they’re pretty happy, and 8 say they’re not too happy. Among the Asian Indian (South Asian) respondents, 7 say they’re very happy, 10 say they’re pretty happy, and 1 said s/he was not too happy. Based on this information, create the table of expected frequencies.

I'd like to know the steps to this answer as well, thanks.

Answer 1

The observed frequency table is as below

Observed	Very Happy	Pretty Happy	Not Too Happy	Total
American Indians	4	15	8	27
Asian Indians	7	10	1	18
Total	11	25	9	45

Each Expected cell Value = (Row Total * Column Total) / Total. Total here = 45

The sum of the rows and columns of the Observed and expected tables must be the same in the end.

Expected	Very Happy	Pretty Happy	Not Very Happy	Total
American Asians	(11*27)/45 = 6.6	(25*27)/45 = 15	(9*27)/45 = 5.4	6.6 + 15 + 5.4 = 27
Asian Indians	(11*18)/45 = 4.4	(25*18)/45 = 10	(9*18)/45 = 3.6	4.4 + 10 + 3.6 = 18
Total	6.6 + 4.4 = 11	15 + 10 = 25	5.4 + 3.6 = 9	45

The Final Table is as Below

Expected Frequency Table	Very Happy	Pretty Happy	Not Very Happy	Total
American Indians	6.6	15	5.4	25
Asian Indians	4.4	10	3.6	18
Total	11	25	9	45