Chapter 1: Q 20. (page 24)

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.

Short Answer

Expert verified

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

Step by step solution

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: $\frac{R o w T o t a l}{T a b l e T o t a l} \times 100$

Part (b) Step 2: Calculation

The table below shows the marginal distribution of parents' smoking habits: Marginal Distribution Percentage: $\frac{R o w T o t a l}{T a b l e T o t a l} \times 100$

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