Solutions Statistics

We are concerned that some data we are using from the General Social Survey may not be representativ

Question: We are concerned that some data we are using from the General Social Survey may not be representative of the true proportion of persons in the United States who are classified by the census as "Black." We know from the census that the population proportion who are "Black" in the U.S. adult population is 13%. We code black persons as "1" and non-black persons as "0." Then we run SPSS one-sample tests, and obtain the following output:

One-Sample Statistics
N Mean Std. Deviation Std. Error Mean
person is black 1500 .1167 .32113 .00829
One-Sample Test
Test Value = .13
t df Sig. (2-tailed) Mean Difference 95% Confidence Interval of the Difference
Lower Upper
person is black -1.608 1499 .108 -.0133 -.0296 .0029

If our null hypothesis is that the proportion of GSS respondents is .13, do we accept or reject this hypothesis at

p = .05? What is your evidence? Would you conclude that the GSS sample is probably representative, or not?

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