Question

A smash or a hit?Researchers asked 150 subjects to recall the details of a car accident they watched on video. Fifty subjects were randomly assigned to be asked, “About how fast were the cars going when they smashed into each other?” For another 50 randomly assigned subjects, the words “smashed into” were replaced with “hit.” The remaining 50 subjects—the control group—were not asked to estimate speed. A week later, all subjects were asked if they saw any broken glass at the accident (there wasn’t any). The table shows each group’s response to the broken glass question.

(a) What proportion of subjects were given the control treatment?

(b) Find the distribution of responses about whether there was broken glass at the accident for the subjects in this study using relative frequencies.

(c) What percent of the subjects were given the “smashed into” treatment and said they saw broken glass at the accident?

Short answer

Part (a) 0.3333

Part (b) 19.33% said YES and 80.67% said NO.

Part (c) 10.67%

Step-by-step solution

Part (a) Step 1. Given information.

The given table is:

Part (a) Step 2. Determine the percentage of individuals who received the control treatment.

Total Subjects included in this study: 150

50 subjects were assigned to each performed treatment. Therefore in the control treatment, 50 subjects were included.

Its proportion is:

$\frac{50}{150}=0.3333$

Part (b) Step 1. Determine the distribution of responses for the individuals concerning whether there was broken glass at the accident. 

First, we need to find the row total for each row,

	“Smashed into”	“Hit”	Control	Row Total
Yes	16	7	6	29
No	34	43	44	121

Yes: A total of 29 subjects responded "YES".

$\frac{29}{150}\approx 0.1933\mathrm{or}19.33\%$

No: A total of 121 subjects responded "NO".

$\frac{121}{150}\approx 0.8067\mathrm{or}80.67\%$

From the above data, we can conclude that about 19.33% of respondents said "YES" and 80.67% said "NO" when they were asked whether they observed broken glasses.

Part (c) Step 1. Determine the percentage of individuals who were given "smashed into" treatment and reported shattered glass.

Total Subjects included in this study: 150

Respondents that said yes to “smashed into” treatment and also observed broken glass include: 16 subjects

Their percentage is:

$\frac{16}{150}\approx 0.1067\mathrm{or}10.67\%$