Question

A researcher reported the results of a telephone poll of 1000 adult Americans. The question posed of those who were surveyed was: "Should the federal tax on cigarettes be raised to pay for health care reform?" Of 600 non-smokers, 362 said yes. Of 400 smokers, 80 said yes. What is the test statistic, at alpha = .05, if you want to determine that the proportion of non-smokers who said yes is greater than the proportion of smokers who said yes?

Answer 1

For non smokers : n1=600 , X1=362

For smokers : n2=400 , X2=80

The sample proportions are ,

p1=X1/n1=362/600=0.6033

p2=X2/n2=80/400=0.2000

The pooled estimate is ,

P=(X1+X2)/(n1+n2)=(362+80)/(600+400)=0.4420

Q=1-P=1-0.4420=0.5580

Let p1 be the population proportion for non smokers and p2 be the population proportion for smokers.

Hypothesis: Vs

The test statistic is ,

The critical value is ,

; from standard normal distribution table

Decision : Here , the value of the test statistic lies in the rejection region.

Therefore , reject Ho

Conclusion : Hence , there is sufficient evidence to support the claim that the proportion of non-smokers who said yes is greater than the proportion of smokers who said yes.