Answer
-.1256 to -.0744
Work Step by Step
We will estimate the population proportion with 99% confidence using a two-sample z-interval with the given information:
n1 = 3500
x1 = 620
n2 = 3497
x2 = 696
sample proportion=$\frac{x_{1}}{n_{2}}$
$\frac{620}{3500}$= .1771| $\frac{696}{3497}$=.2771
z score is 2.575 since the confidence interval is 99%
(.1771 -.2771 )+2.575 sqrt($\frac{.1771(1−.1771)}{3500}$+ $\frac{.2771(1−.2771)}{3497}$=-.1256
(.1771 -.2771 )-2.575 sqrt($\frac{.1771(1−.1771)}{3500}$+ $\frac{.2771(1−.2771)}{3497}$=-.0744
This means that we are 99% confident that the true proportion between all 9th and 12th-grade students who smoked marijuana in the last 30 days is between -.1256 and -.0744
