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Statistics: U.S. Social Problems

2. The issue of how much should be spent to solve particular U.S. social problems is a complex matter and people have diverse and conflicting ideas on these issues. Race and social class have an impact on how people perceive the extent of government spending. The 2006 GSS contains several questions on these topics. For this exercise, we present race and the variable NATFARE which asked whether we were spending too much, too little, or the right amount of money to address welfare.

Spending on welfare Race of respondent
White Black Hispanic Total
Too little 128 41 21 190
About right 197 32 21 250
Too much 185 31 19 235
Total 510 104 61 675

4. We continue our analysis from Exercise 2, this time examining the relationship between social class (CLASS) and spending on welfare (NATFARE).
a) What is the number of degrees of freedom for this table?
b) Calculate the chi-square. Based on an alpha of 0.01, do you reject the null hypothesis? Explain the reason for your answer.

Social class
Lower class Working class Middle class Upper class Total
Too little 23 92 76 8 199
About right 12 113 133 10 268
Too much 12 127 99 7 245
Total 47 332 308 25 712

Solution Preview

Please find attached word file with step by step explanation of the chi squared test for independence as well as a thorough step by step solution of the problems in question.

The Chi squared test (X2 test) for independence (sometimes called the Pearson chi squared test) tests the association (connection) between two categorical variables.

The Null hypothesis H0 is that the one categorical variable does not affect the other categorical variable and thus they are independent (not associated).

With the alternative hypothesis Ha being that the one categorical variable affects the other categorical variable and thus they are dependent (associated).

In the case of this question perception on "spending on welfare by government" i.e. too little, about right and too much are the one categorical data and "race of ...

Solution Summary

A step by step explanation, with the use of two examples, of the chi squared test of independence demonstrating the calculation of the expected values, the determination of the degrees of freedom as well as the evaluation of the test statistic and the acceptance or rejection of the null hypothesis for independence with the use of statistical tables.