The General Social Survey (GSS) at http: //gss.norc.org is a sociological survey

Question

The General Social Survey (GSS) at http: //gss.norc.org is a sociological survey used to collect information and keep a historical record of the concerns, experiences, attitudes, and practices of residents in the United States. The GSS was first conducted in 1972 and was conducted almost annually (with the exceptions of the years 1979, 1981, and 1992) until 1994. Since 1994, the GSS has been conducted in even numbered years. Every GSS includes the question, 'Taken all together, would you say that you are very happy, pretty happy, or not too happy?" The following table shows the responses to the question cross-tabulated with family income information in 2008 (Agresti, Alan and Franklin, Christine, 2013, Statistics: The Art and Science of Learning from Data, p. 97). a. What percent of people in the table are pretty happy or have average family income? b. What percent of people in the table have family income above average? c. What is the marginal distribution (in percentage) of types of happiness? d. What is the conditional distribution (in percentage) of types of happiness for people whose family income is below average?

Explanation / Answer

Following table shows the row total and column total:

(a)

Out of 1993, 1089 are pretty happy, 883 has average family income and 233 has pretty happy and have average family income so requried percentage is

(1089 +883 - 233) /1993 = 0.8726 = 87.26%

(b)

Out of 1993, 423 have above average family income so requried percentage is

(423) /1993 = 0.2122 = 21.22%

(c)

The marginal distribution of type of happiness is

(d)

Following is the required conditional distribution:

Types of Happiness Family income Not too happy Pretty Happy Very Happy Total Above average 26 233 164 423 average 117 473 293 883 below average 172 383 132 687 Total 315 1089 589 1993

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