Question

In: Statistics and Probability

Studies have shown that people who are using safety equipment when engaging in an activity tend...

Studies have shown that people who are using safety equipment when engaging in an activity tend to take increased risks. Will risk taking increase when people are not aware they are wearing protective equipment and are engaged in an activity that cannot be made safer by this equipment? Participants in the study were falsely told they were taking part in an eye-tracking experiment for which they needed to wear an eye-tracking device. Eighty subjects were divided at random into two groups of 40 each, with one group wearing the tracking device mounted on a baseball cap and the other group wearing it mounted on a bicycle helmet. Subjects were told that the helmet or cap was just being used to mount the eye tracker. All subjects watched an animated balloon on a video screen and pressed a button to inflate it. The balloon was programmed to burst at a random point, but until that point, each press of the button inflated the balloon further and increased the amount of fictional currency a subject would earn. Subjects were free to stop pumping at any point and keep their earnings, knowing that if the balloon burst, they would lose all earnings for that round. The score was the average number of pumps on the trials, with lower scores corresponding to less risk taking and more conservative play. Here are the first 10 observations from each group.

Helmet: 3.67 36.50 29.28 30.50 24.08 32.10 50.67 26.26 41.05 20.56

Baseball Cap: 29.38 42.50 41.57 47.77 32.45 30.65 7.04 2.68 22.04 25.86

Compare the distributions for the two groups. How is wearing of a helmet related to the measure of risk behavior? Hint: Create side by side box and whisker plots.


Solutions

Expert Solution

The side-by-side box and whisker plots for the two distributions are drawn and it is seen from the plots that in the observations of the group having helmet, the distribution is slightly positively skewed, evident from the long upper whisper with an outlier lying below the first quartile which indicates that there is a decreased rate in the tendency of taking risks using a helmet.

Also, in the second group of observations wearing a baseball cap, the distribution is negatively skewed, evident from the longer lower whisker, also, the range of the distribution is quite high, evident from the size of the box. No outlier is present here. And this shows that there is an increased rate in the tendency of taking risks using a baseball cap as that compared to wearing a helmet.

The box and whisker plots are obtained using R-software. Code and output are attached below for verification.

orchestra answered 1 year ago
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