The table shows GSS data on happiness and the number of close friends, with expected cell counts given underneath the observed counts.

a. Suppose the variables were independent. Explain what this means in this context.
b. Explain what is meant by an expected cell count. Show how to get the expected cell count for the first cell, for which the observed count is 34.
c. Compare the expected cell frequencies to the observed counts. Based on this, what is a profile of subjects who tend to be
(i) More happy than independence predicts and
(ii) Less happy than independence predicts.

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Happines Number of Close Frlends 0-1 Not Too Pretty Happy Very Happy Happy Total 169 19.2 95.1 418 394.6 54.7 5 79.5 226.9 6 or more 576 186.4 65.3 164 324.3 814 Total 1446