The 1998 General Social Survey asked a sample of adult American whether they think the federal government spends too little, the right amount, or too much money on various programs. The responses concerning the space program, categorized by political leaning, are summarized in the table below. It is thought that liberals believe the government is better at making the policies and spending for their enforcement whereas conservatives believe more in individual responsibility. This is an idea they wanted to test.
The survey results are as follows.
Liberal Moderate Conservative Total
Too little 50
47 36 133
Just right 164
214 212 590
Too much 162
174 176 512
435 424 1235
A. State your hypothesis for applying the chi-square test to this table of data. Remember to think in terms of what the original question or issue is.
B. What does the test reveal about a possible relationship between political leanings and opinion about federal spending on the space program?
a. What is the test statistic?
b. What is the critical value for X2?
c. Do the different political groups seem to have different opinions on this issue? Explain.
By itself, the chi-square test determines only whether the data provide evidence of a relationship between the two variables. If the result is significant, one can go on to identify the source of that relationship by finding the cells of the table that contribute the most to the X2 value (i.e., those cells with the biggest discrepancy between the observed and expected counts) and by noting whether the observed count falls above or below the observed count in those cells.
In the above study, the survey also asked other questions about the level of government spending. The following table reports survey responses to a question about the level of the federal government's spending on the environment, with respondents classified according to their political leaning. Again, it was thought that a person's political leanings might influence how they felt about the government's spending levels in areas they personally might be concerned with or have strong opinions of .
Liberal Moderate Conservative Total
Too little 292 271 239 802
Just right 85 142 133 360
Too much 11 27 64 102
Totals 388 440 436 1264
A. Conduct a chi-square test of whether opinions about spending on the environment are related to political leaning. Be sure to state your hypothesis, test statistic and critical value for X2.
B. Is the test result significant at
a. the 0.05 level?
b. the 0.01 level?
c. the 0.005 level?
C. If the test is significant, identify the three cells that make the largest contribution to the test statistic. (you can use the other matrix - B - in your calculator to get at the larger numbers) Also indicate whether the observed count exceeds or falls short of the expected count for each of those cells.
a. What is significant about the observed exceeding or falling short of the expected count for those cells?
D. Write a paragraph summarizing your findings for this second test. Refer back to your hypothesis about the independence of political leanings and people's opinion on the government's spending on environmental issues
E. Compare your findings with regard to spending on the environment with those about spending on the space program above.
a. What do they say about the attitudes of people on spending?
Step by step method for testing the hypothesis under 5 step approach is discussed here. Excel template for each problem is also included. This template can be used to obtain the answers of similar problems.