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 are the results 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

$p_1=\frac{362}{600}=0.6033,\;\;p_2=\frac{80}{400}=0.2,\;\; p_0=\frac{362+80}{600+400}=0.442.$

Null hypothesis $H_0: p_1=p_2.$

Alternative hypothesis $H_a:p_1>p_2 .$

Test statistic: $z=\frac{p_1-p_2}{\sqrt{p_0(1-p_0)(\frac{1}{n_1}+\frac{1}{1/n_2}})}= \frac{0.6033-0.2}{\sqrt{0442(1-0.442)(\frac{1}{600}+\frac{1}{400}})}=12.58.$

P-value: $p<0.0001.$

Since the P-value is less than 0.05, reject the null hypothesis.

There is a sufficient evidence that the proportion of non-smokers who said yes is greater than the proportion of smokers who said yes.