A study claims that the percentage of incomes that people pay in total taxes is
ID: 3204759 • Letter: A
Question
A study claims that the percentage of incomes that people pay in total taxes is the same for different income levels. A "random sample" of tax data showing the average taxes paid in six different cities is given below; the column heading is the income level. a) Form an explicit null hypothesis and perform an ANOVA test to evaluate this claim. b) Discuss some difficulties with this "random" sample - since we are picking cities, how does it affect the statement of the null hypothesis? $25,000 $50,000 $75,000 income level income level income level Des Moines, IA 7.4 8.2 9 Charleston, WV 6.8 7.1 8.5 Memphis, TN 6.9 5.8 6 Sioux Fall, SD 7.3 6.4 7.1 Philadelphia, PA 15.8 15.2 15.1 Chicago, IL 11.8 11.9 12.4 Chapter 10: 19, 22, 27
Explanation / Answer
(a)
Here we need to compare mean value of three groups so one way ANOVA analysis will be used. Hypotheses are:
H0: The percentage of incomes that people pay in total taxes is the same for different income levels.
Ha: The percentage of incomes that people pay in total taxes is not same for different income levels.
Following is the output of one way ANOVA analysis generated by excel:
The test statistics is
F = 0.04
P-value is: 0.9611
Since p-value is greater than 0.05 so we fail to reject the null hypothesis.
That is on the basis of sample evidence we cannot conclude that the percentage of incomes that people pay in total taxes is the same for different income levels.
(b)
It may be possible that in some cities tax level is same for all income groups and in other cities it is not. So these samples may not represent true population.
One factor ANOVA Mean n Std. Dev 9.33 6 3.691 income level, $25000 9.10 6 3.689 income level, $50000 9.68 6 3.430 income level, $75000 9.37 18 3.396 Total ANOVA table Source SS df MS F p-value Treatment 1.034 2 0.5172 0.04 .9611 Error 194.982 15 12.9988 Total 196.016 17Related Questions
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