18. Suppose we are interested in comparing the proportion of male students who smoke to the proportion of female students who smoke. We have a random sample of 150 students (60 males and 90 females) that includes two variables: Smoke = "yes" or "no" and Gender = "female (F)" or "male (M)". The two-way table below summarizes the results:
Smoke = Yes Smoke = No Sample Size
Gender = M 9 51 60
Gender = F 9 81 90
(a) If the parameter of interest is the difference in proportions, pm - pf, where pm and pf represent the proportion of smokers in each gender, find a point estimate for this difference in proportions based on the data in the table. Report your answer with two decimal places.
(b) Below is a bootstrap distribution using 1000 samples.
Bootstrap Dotplot of p1 - p2
samples = 1000
mean = 0.050
std. error = 0.055
Use the estimate of the standard error to construct a 95% confidence interval for the difference in the proportion of smokers between male and female students, pm - pf. Provide an interpretation of the interval in the context of this data situation.