Question

Philip Morris wishes to determine if there is a difference between the proportion of women and proportion of men who smoke cigarettes. Random samples of 125 women and 140 men reveal that 13 women and 5 men smoke cigarettes. Does the data indicate that the proportion of women who smoke cigarettes is higher than the proportion of men who do at α=.01?

What is the 95% confidence interval for p_Women - p_Men?

	a.	(0.0066, 0.1300)
	b.	(0.0174, 0.1192)
	c.	(0.0076, 0.1290)
	d.	None of the answers is correct
	e.	(0.0165, 0.1201)

Answer 1

Let P1 and P2 be the respective population proportions for women and men respectively.

The null and alternate hypothesis are:

H0:

Ha:

The test statistic value is given by:

Since this is a right-tailed test, so the p-value is given by:

Since p-value is greater than 0.01, so we do not have sufficient evidence to reject the null hypothesis
H0. Thus the data does not indicate that .

Now,

we know that the 95% confidence interval for difference of proportions is given by:

Hence option A.