Question

Help with AP Statistics?? Will medal and fan!!!

A random sample of 250 men yielded 175 who said they'd ridden a motorcycle at some time in their lives, while a similar sample of 215 women yielded only 43 that had done so. Find a 99% confidence interval for the difference between the proportions of men and women who have ridden motorcycles.

A. .5 ± .103
B. .5 ± .085
C. .5 ± .112
D. .4688 ± .085
E. .5 ± .078

Answer 1

which proportion deals with .5 ? that appears to be the most obvious way to narrow this.

Answer 2

I am torn between A and C, as I have gotten both answers while doing this problem.

Answer 3

use:\[z=\frac{x-mean}{(sd)/\sqrt n}\]
use:\[mean\pm z(sd)/\sqrt n=x\]

Answer 4

do you recall the z score for the 99% CI?

Answer 5

the sd in this case will conform to:\[\sqrt{.5*.5}\] and n is the sample size that gives us the .5 to begin with.

Answer 6

im reading it off .... you have a 2 sample proportion ...

Answer 7

the sd will be the sqrt of the sum of their variances ....

Answer 8

\[(sd)/\sqrt n=\sqrt{\frac{p_0q_0}{n_0}+\frac{p_1q_1}{n_1}}\]

Answer 9

sqrt(175(250-175)/250^3+43(215-43)/215^3) is about .0398, and the zscore of 2.576 gives us a margin of error as: .1025 so thats about our add on to the mean

Answer 10

http://www.wolframalpha.com/input/?i=2.576*sqrt%28175%28250-175%29%2F250%5E3%2B43%28215-43%29%2F215%5E3%29

Answer 11

Thanks for your help @amistre64, so it would be A?

Answer 12

with any luck, yes :)

Answer 13

@amistre64 Thank you! You have been a great help!