Question

3a. Time magazine conducted a telephone poll and asked the question "Should the federal tax on cigarettes be raised to pay for health care reform?" Of the 605 non-smokers polled in 351 said yes and 101 of the 195 smokers said yes. Is there enough evidence to state there is a difference between the proportion of smokers and non-smokers who believe the federal tax on cigarettes should be raised to pay for health care reform?

b. You share your results with your friend who has not taken statistics. Your friend says, "it's obvious that a lower percentage of smokers believe the tax should be raised. Why are you saying they are the same?" Answer your friend so he/she will understand the conclusion you made in part a.

Answer 1

3a.

Test and CI for Two Proportions

Sample X N Sample p
Non Smokers 351 605 0.580165
Smokers 101 195 0.517949

p(1): population proportion of "Yes" for non-smokers

p(2): population proportion of "Yes" for smokers
Difference = p (1) - p (2)

Null hypothesis, H0: p(1)-p(2)=0 vs Alternative hypothesis, H1: p(1)-p(2) not = 0
Estimate for difference: 0.0622166
Test for difference = 0 (vs not = 0): Z = 1.52 P-Value = 0.128

Fisher's exact test: P-Value = 0.135

95% CI for difference: (-0.0181897, 0.142623)

Since P-value>0.05 so we fail to reject null hypothesis and conclude that there is not enough evidence to state there is a difference between the proportion of smokers and non-smokers who believe the federal tax on cigarettes should be raised to pay for health care reform.

b. It is obvious that a lower percentage of smokers believe the tax should be raised however this is difference is not stratistically significant and since zero is contained by 95% C.I. for difference so we are 95% confident that there is insignificant difference between the proportion of smokers and non-smokers who believe the federal tax on cigarettes should be raised to pay for health care reform.