The New York Times reported a result of a telephone survey o

The New York Times reported a result of a telephone survey of 800 Americans. The survey asked Americans \"Should the State tax on cigarettes be raised to pay for health care reform?\" The survey results are shown on the right. Is there evidence at the = 0.01 level of significance that non-smokers are significantly more likely to endorse raising taxes on cigarettes to pay for health care than smokers?

Solution

Doing an Expected Value Chart,          
          
47.2875       147.7125
146.7125   458.2875
          
Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    1.45935724      
          
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 =    0.01      
          
chi^2(critical) =    6.634896601      
          
Also, the p value is          
          
P =    0.227032418      
          
Thus, comparing chi^2 and chi^2(crit) [or, p and significance level], we   FAIL TO REJECT THE NULL HYPOTHESIS.      

Thus, we conclude that there is no signficant evidence at 0.01 significance that non-smokers are significantly more likely to endorse raising taxes on cigarettes to pay for health care than smokers. [CONCLUSION]