Table below shows the results where subjects were asked whether, to help the environment, they would be willing to (1) pay higher taxes, or (2) accept a cut in living standards.
Cut Living standards
Pay higher Taxes Yes No Total
Yes 113 66 179
No 54 339 393
Total 167 405 572
a. Perform a statistical test for whether there is an association between the two ways to help the environment, "cut living standards" and "pay higher taxes". Explain your results.
b. What is the estimated OR (odds ratio) between favoring cutting living standards and paying higher taxes? What is the 95% confidence interval for the true odds ratio?
c. Suppose the results on the two questions came from two independent samples of 572 each (i.e. the two questions were answered by different people). Perform a statistical test on the independence of the two variables. Estimate the OR between favoring cutting living standards and paying higher taxes, and obtain its 95% Confidence interval. Compare your results with a and b, and comment on how the use of dependent samples can improve precision.