A recent sample of adults was asked their opinions regarding government spending
ID: 3133850 • Letter: A
Question
A recent sample of adults was asked their opinions regarding government spending on health and government spending on law enforcement. The data are in the table below.
Law Enforcement Spending
Health Spending
Increase
Decrease
Total
Increase
292
25
317
Decrease
14
9
23
Total
306
34
340
Test whether increased spending is favored in one area. Use a 5% level of significance. 1) Write out the appropriate null hypothesis and the alternative hypothesis; 2) Calculate the test statistic (show your work); 3) Give your conclusion including a comparison to alpha or the critical value
Law Enforcement Spending
Explanation / Answer
1.
Here,
Ho: Increased spending is not favored in one area.
Ha: Increased spending is favored in one area.
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2.
Doing an Expected Value Chart,
Using chi^2 = Sum[(O - E)^2/E],
chi^2 = 23.25942181 [ANSWER, TEST STATISTIC]
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With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,
a = 2
b = 2
df = 1
Thus, the critical value is
significance level = 0.05
chi^2(critical) = 3.841458821
As chi^2 > 3.841, we REJECT THE NULL HYPOTHESIS.
Thus, there is significant evidence that increased spending is favored in one area at 0.05 level. [CONCLUSION]
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