Q 32. - The Practice of Statistics for AP

Question

National Survey of Adolescent Health interviewed several thousand teens (grades 7 to 12). One question asked was “What do you think are the chances you will be married in the next ten years?” Here is a two-way table of the

responses by gender: 

Your percent from the previous exercise is part of

(a) the marginal distribution of gender.

(b) the marginal distribution of opinion about marriage.

(c) the conditional distribution of gender among adolescents with a given opinion.

(d) the conditional distribution of opinion among adolescents of a given gender.

(e) the conditional distribution of females among those who said “Almost certain. 

Step-by-Step Solution

Answer

The correct option is (c) the conditional distribution of gender among adolescents with a given opinion.

Step 1: Given information

The given picture displays the responses by gender 

	Female	Male
Almost no chance	119	103
Some chance, but probably not	150	171
A 50-50 chance	447	512
A good chance	735	710
Almost certain	1174	756

Step 2: Concept

The distribution of a category variable is displayed using pie charts and bar graphs. Any set of quantities measured in the same units can be compared using bar graphs. It's a good idea to ask yourself, "What do I see?" when looking at any graph.  

Step 3: Calculation

	F	M
	No.	Percentage	No.	Percentage
Almost no chance	119	$\frac{119}{119+103}=53.60\%$	103	$\frac{103}{119+103}=46.40\%$
Some chance, but probably not	150	$\frac{150}{150+171}=46.73\%$	171	$\frac{171}{150+171}=53.27\%$
A 50-50 chance	447	$\frac{447}{447+512}=46.61\%$	512	$\frac{512}{447+512}=53.39\%$
A good chance	735	$\frac{735}{735+710}=50.87\%$	710	$\frac{710}{735+710}=49.13\%$
Almost certain	1174	$\frac{1174}{1174+756}=60.83\%$	756	$\frac{756}{1174+756}=39.17\%$
Total	2625	$\frac{2625}{4877}=53.82\%$	2252	$\frac{2252}{4877}=46.18\%$

The $\%$ is part of the conditional gender distribution among adolescents with a particular viewpoint. As a result, option (c) is correct.