some people want to comapre the proportion of high school boys that smoke cigarettes to the proportion of high school girls that smoke cigarettes.

Question

some people want to comapre the proportion of high school boys that smoke cigarettes to the proportion of high school girls that smoke cigarettes. use the data below to test the claim that the proportion of boys that smoke is 5% bigger than the proportion for girls. 

 

Smoke     girls         boys

 

yes          407         470

 

no            1451        1469

Answer 1

As Christian shows, the proportions of each that smoke can be calculated as:

 

boys who smoke = 470 / (470+1469) = 0.242 --> 24.2 %

 

girl who smoke = 407 / (407+1451) = 0.219 -->  21.9 %

 

It's a little ambiguous what this phrase means: "the proportion of boys that smoke is 5% bigger than the proportion for girls".

 

1) It could mean that the boys' proportion as a percent is 5 more (percent) than the girls' proportion as a percent.  With this interpretation the boys percentage is not 5% more than the girls', it's only 2.3% larger.

 

2) The other interpretation of 5% bigger (that Christian suggests) is increasing the girls' proportion by adding 0.05 times its value to itself, this is the same as multiplying by 1.05.  So that would be:  0.219 * 1.05 = 0.230 .

In this case the boys' proportion is greater than 5% more than the girls'.

 

I'm torn about which of these to recommend as the answer, it's your choice!