Question

1. 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 wasnt any). the table shows each groups response to the broken glass question.14 treatment \smashed into\ \hit\ control response yes 16 7 6 no 34 43 44 (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?

Explanation:

Step1: Calculate proportion for control treatment

The total number of subjects is 150 and the number of subjects in the control group is 50. The proportion is calculated as $\frac{\text{Number of control - group subjects}}{\text{Total number of subjects}}$.

Step2: Calculate relative - frequencies for responses

First, find the total number of 'Yes' and 'No' responses across all groups. Then calculate the relative frequency for each response category as $\frac{\text{Number of responses in a category}}{\text{Total number of responses}}$.

Step3: Calculate percentage for "smashed into" and "Yes"

The number of subjects given "smashed into" treatment and said "Yes" is 16, and the total number of subjects is 150. The percentage is calculated as $\frac{\text{Number of relevant subjects}}{\text{Total number of subjects}}\times100\%$.

Answer:

(a) The proportion of subjects given the control treatment is $\frac{50}{150}=\frac{1}{3}\approx0.333$.
(b)

• Total number of 'Yes' responses: $16 + 7+6=29$
• Total number of 'No' responses: $34 + 43+44 = 121$
• Total number of responses: $29 + 121=150$
• Relative frequency of 'Yes' responses: $\frac{29}{150}\approx0.193$
• Relative frequency of 'No' responses: $\frac{121}{150}\approx0.807$

(c) The percentage of subjects given the "smashed into" treatment and said they saw broken glass is $\frac{16}{150}\times100\%=\frac{1600}{150}\approx10.67\%$.