Question

A survey was conducted to investigate whether alcohol consumption and smoking are related. In a random sample of 300 smokers, 196 said they had consumed alcohol at least once in the past week. In an independent random sample of 300 non-smokers, 159 said they had consumed alcohol in the past week. If $p$, is the proportion of smokers in the population who have had a drink in the past week and $p_w$ is the corresponding proportion of non-smokers, then a test of the hypotheses $H_0: p_3-p_w=0$ against the two-sided alternative produces a test statistic of $z=3.07$ and a $P$-value of $0.002$. If we had instead analyzed these results with a chi-square test of homogeneity, which of the following would be the test statistic and $P$-value?
a. $\chi^2=9.42, P$-value $=0.002$
b. $\chi^2=9.42, P$-value $=0.004$
c. $\chi^2=3.07, P$-value $=0.004$
d. $x^2=1.75, P$.value $=0.002$
e. $x^2=1.75, P$.value $=0.004$