Chapter 3, Problem 52CR

a.

To determine

Construct a comparative bar chart for the data using relative frequencies.

Answer to Problem 52CR

The comparative bar chart is given below:

Explanation of Solution

Calculation:

The data represents the responses regarding the perceived harm of smoking for the groups smokers, former smokers, and nonsmokers.

The general formula for the relative frequency is as follows:

$\text{Relative}\text{Frequency = }\frac{\text{Frequency}}{\text{Total frequency}}$

Substitute the frequency for the responses as “vary harmful” and the total frequency for smokers as “241” in relative frequency.

$\begin{array}{c}\text{Relative}\text{Frequency}\text{for the response very harmful for smokers}=\frac{145}{241}\\ =0.602\end{array}$

Relative frequencies for the remaining responses are obtained below:

Perceived Risk of Smoking	Relative Frequency
	Smokers	Former Smokers	Nonsmokers
Very harmful	$\frac{145}{241}=0.602$	$\frac{204}{261}=0.782$	$\frac{432}{502}=0.861$
Somewhat harmful	$\frac{72}{241}=0.299$	$\frac{42}{261}=0.161$	$\frac{50}{502}=0.100$
Not too harmful	$\frac{145}{241}=0.071$	$\frac{10}{261}=0.038$	$\frac{15}{502}=0.030$
Not at all harmful	$\frac{7}{241}=0.029$	$\frac{5}{261}=0.019$	$\frac{5}{502}=0.010$

Software procedure:

Step-by-step procedure to draw comparative bar graph using MINITAB software:

• Choose Graph > Bar Chart
• From Bars represent, choose Values from a table.
• Under Two-way table, choose Cluster. Click OK.
• In Graph variables, enter the column of Smokers, Former Smokers, and Nonsmokers.
• In Row labels, enter the column of 'Risk of smoking'.
• In Table Arrangement, choose Rows are outermost categories and columns are innermost.
• Click OK.

b.

To determine

Comment on how smokers, former smokers, and nonsmokers differ with respect to perceived risk of smoking.

Explanation of Solution

From the comparative bar chart, it is observed that, most number of non-smokers have the belief that smoking is very harmful. For other three groups, the difference between the believes of smokers, non-smokers, and former smokers are almost same and the frequency is very less.