Q 20. - The Practice of Statistics for AP

Question

Smoking by students and parents Here is data from a survey conducted at eight high schools on smoking among students and their parents:

(a) How many students are described in the two-way table? What per cent of these students smoke?

(b) Give the marginal distribution of parents’ smoking behaviour, both in counts and in percentages.

Step-by-Step Solution

Answer

Part (a) Table describes a total of $5375$ students $18.7\%$ of students smoke.

Part (b) The table is 

Marginal distribution table
Parents smoking behavior	Student does not smoke	Student smokes	Row total	Percentage
Neither parents smoke	1168	188	1356	$\frac{1356}{5375}$	0.2523	$\frac{1356}{5375}\times 100$	36.8%
one parent smoke	1823	416	2239	$\frac{2238}{5375}$	0.4166	$\frac{2238}{5375}\times 100$	24.1%
Both parents smoke	1380	400	1780	$\frac{1780}{5375}$	0.3312	$\frac{1780}{5375}\times 100$	39.1%
Total	4371	1004	5375		1		100

Part (a) Step 1: Given Information

	Neither parent smoke	one parent smoke	Both parents smoke
Student does not smoke	1168	1823	1380
Student smoke	188	416	400

Part (a) 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. 

Part (a) Step 3: Calculation

The table describes a total of $5375$ students. $18.7\%$ of students smoke.

Hence, the table describes a total of $5375$ students. $18.7\%$ of students smoke. 

	Parent's smoking
	Neither parent smoke	One parent smoke	Both parent smoke	Total	Percent
Student does not smoke	1168	1823	1380	4371	$\frac{4371}{5375}\times 100=81.3\%$
student smoke	188	416	400	1004	$\frac{1004}{5375}\times 100=18.7\%$
Total	1356	2239	1780	5375
Percent	25.2%	41.7%	33.1%

Part (b) Step 1: Concept

Marginal Distribution Percentage: $\frac{Row Total}{Table Total }\times 100$

Part (b) Step 2: Calculation

The table below shows the marginal distribution of parents' smoking habits: Marginal Distribution Percentage: $\frac{Row Total}{Table Total} \times 100$

Table Total=$5375$

As a result, the marginal distribution of parents' smoking habits is displayed. 

Marginal distribution table
Parents smoking behavior	Student does not smoke	Student smokes	Row total	Percentage
Neither parents smoke	1168	188	1356	$\frac{1356}{5375}$	0.2523	$\frac{1356}{5375}\times 100$	36.8%
one parent smoke	1823	416	2239	$\frac{2238}{5375}$	0.4166	$\frac{2238}{5375}\times 100$	24.1%
Both parents smoke	1380	400	1780	$\frac{1780}{5375}$	0.3312	$\frac{1780}{5375}\times 100$	100%
Total	4371	1004	5375		1