Question

Time magazine reported the result of a telephone poll of 800 adult Americans. The question posed of the Americans who were surveyed was: "Should the federal tax on cigarettes be raised to pay for health care reform?" Of the 195 smokers, 56 said “yes” to the question. Of the 605 non-smokers, 251 said “yes” to the question. Is there sufficient evidence at the  = .02 level, say, to conclude that the non-smokers are more willing to raise taxes on cigarettes than smokers? (define clearly, Be clear in your conclusion, show all work)

Answer 1

p1cap = X1/N1 = 56/195 = 0.2872
p1cap = X2/N2 = 251/605 = 0.4149
pcap = (X1 + X2)/(N1 + N2) = (56+251)/(195+605) = 0.3838

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 < p2

Rejection Region
This is left tailed test, for α = 0.02
Critical value of z is -2.05.
Hence reject H0 if z < -2.05

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.2872-0.4149)/sqrt(0.3838*(1-0.3838)*(1/195 + 1/605))
z = -3.19

P-value Approach
P-value = 0.0007
As P-value < 0.02, reject the null hypothesis.

answered by: anonymous