Question

A smash or a hit Refer to Exercise 23.

(a) Find the distribution of responses about whether there was broken glass at the accident for each of the three treatment groups. Make a segmented bar graph to compare these distributions.

(b) Describe what the graph in part (a) reveals about the association between response about broken glass at the accident and treatment received for the subjects in the study.

Short answer

Part (a)

	"Smashed into”	“Hit”	Control
Yes	32%	14%	12%
No	68%	86%	88%

Part (b)

In comparison to the other two treatments, the proportion of individuals who reported broken glass at the accident is substantially higher for the "Smashed into" treatment and the responses to the "Hit" treatment and the Control treatment do not appear to differ much.

Step-by-step solution

Part (a) Step 1. Given information.

The given table is:

Part (a) Step 2. Find the distribution of responses for each of the three treatment groups

The trial contains 150 participants, with 50 assigned to each treatment.

We divided each count by 50 to establish the distribution of responses for each of the three treatment groups, as each treatment has 50 subjects.

	"Smashed into”	“Hit”	Control
Yes	$\frac{16}{50}=0.32\mathrm{or}32\%$	$\frac{7}{50}=0.14\mathrm{or}14\%$	localid="1653402468422" $\frac{6}{50}=0.12\mathrm{or}12\%$
No	$\frac{34}{50}=0.68\mathrm{or}68\%$	$\frac{43}{50}=0.86\mathrm{or}86\%$	$\frac{44}{50}=0.88\mathrm{or}88\%$44

Part (a) Step 3. Construct a segmented bar graph.

Each bar must be the same width and have the same height as the percentage.

Part (b) Step 1. Describe the association between response about broken glass at the accident and treatment received.

The proportion of subjects who indicated they witnessed broken glass at the accident is substantially greater for the "Smashed into" treatment than for the other two treatments (as the yellow section of the bar graph for Smashed into is the highest).

We also note that there does not appear to be a significant difference in reactions between the "Hit" and the "Control" treatments, as the bars corresponding to those treatments are extremely comparable.