Question

A concern in allowing the tinting of car front side windows is that tasks performed through these windows often require the rapid detection of low-contrast, unillumitated targets. If the tinting interferes with detection of targets then road safety may be compromised.

A random sample of 182 US adults was selected to participate in a study. Participants were randomly assigned to drive a car with a predetermined degree of tinting on the front side windows of the car (none: no window tinting, low: low window tinting, and high: high window tinting). For each participant, the inspection time was recorded (inspection time is defined as the time required to perform a simple discrimination task through the treated windows (in milliseconds)). Many variables were recorded for each participant, however we will focus our attention on the following variables:

1.       Tint (degree of window tinting: none= no window tinting, low= low window tinting, high= high window tinting)

2.       Inspect (inspection time (milliseconds)

The histogram for the distribution of inspection times for the 182 US adults and the numerical summaries by tint level and overall are provided below. Use this information to answer the following questions.  

Histogram of Inspection times for 182 US adults by MB CN 50 100 150 200 Inspection time (milliseconds)

1. You want to provide a complete summary that describes the distribution of inspection time. Please select the most appropriate description.

• Based on the histogram, the distribution of inspection time for the 186 sampled US adults is skewed to the right and unimodal with some possible outliers. The appropriate center is the mean which has a value of 60.6 milliseconds. The appropriate spread is provided by the standard deviation with a value of 39.2 milliseconds.

• Based on the histogram, the distribution of inspection time for the 186 sampled US adults is skewed to the right and unimodal. The appropriate center is the mean which has a value of 60.6 milliseconds. The appropriate spread is provided by the standard deviation with a value of 39.2 milliseconds.

• Based on the histogram, the distribution of inspection time for the 186 sampled US adults is skewed to the right and unimodal with some possible outliers. The appropriate center is the median which has a value of 47.3 milliseconds. The overall range is from 17.7 milliseconds to 210 milliseconds and the interquartile range is 41.3 milliseconds (ranges from 34.3 milliseconds to 75.6 milliseconds).  

• Based on the histogram, the distribution of inspection time for the 186 sampled US adults is skewed to the right and unimodal. The appropriate center is the median which has a value of 47.3 milliseconds. The overall range is from 17.7 milliseconds to 210 milliseconds and the interquartile range is 41.3 milliseconds (ranges from 34.3 milliseconds to 75.6 milliseconds).

2. Of the drivers driving a car with no window tinting,  75% had an inspection time of at most _____________ milliseconds.

• 17.7

• 32.4

• 43.1

• 59.9

• 174

3. Consider the following two drivers:

• Driver A was driving a car with a high level of window tinting and had a recorded inspection time of 197 milliseconds
• Driver B was driving a car with a low level of window tinting and had a recorded inspection time of 187 milliseconds.  

Which of these two drivers is “most extreme” with respect to the level of window tinting? (that is, which inspection time is the farthest from the mean inspection time for that level of window tinting in terms of standard deviations).

• Both drivers A and B.

• Driver A

• Driver B

• It can not be determined with the information provided.

Answer 1

1. ANS: Based on the histogram, the distribution of inspection time for the 186 sampled US adults is skewed to the right and uni-modal. The appropriate center is the median which has a value of 47.3 milliseconds. The overall range is from 17.7 milliseconds to 210 milliseconds and the inter-quartile range is 41.3 milliseconds (ranges from 34.3 milliseconds to 75.6 milliseconds).

2. Of the drivers driving a car with no window tinting,  75% had an inspection time of at most 59.9 milliseconds.

3. ANS: Driver B.

Here Z-score for both the drivers are

For driver A,

i.e. The inspection time is 2.7350 standard deviations above the mean.

For driver A,

X-μ 187-60 Z33.7 3.7685

i.e. The inspection time is 3.7685 standard deviations above the mean.

So Driver B is “most extreme” with respect to the level of window tinting