Variables and Simulation Study in Statistics

Part 1: Dataset Analysis

1.Suppose a data set gives information on 35 different colleges in Minnesota. For each of the 35 colleges, the data set reports the type (private or public), the admission rate (%), the number of undergraduates enrolled, and the annual cost for tuition (in dollars).

a.What are the observational units here?  

b.Classify each of the four variables described above as numerical or categorical.  

Type -
Admission Rate -
Number of Undergraduates Enrolled -
Annual Cost for Tuition -

c.For each of the following, specify whether it is a legitimate variable for the observational units you specified in part a. 

The highest tuition cost amongst all the colleges.
Whether or not the admission rate is below 50%.
The average number of students enrolled across all the colleges.
The proportion of the colleges with an admission rate below 50%.

2.A recent study was conducted to investigate the demographic distribution of individuals who wore their face mask improperly in public. One theory is that fewer adults of advanced age (who are more susceptible to COVID-19 complications) will wear their face mask improperly. Between June and September of 2020, researchers performed observations at different times and weekdays in three German (Regensburg, Augsburg, and Berlin), one Austrian (Vienna), and one Polish city (Szczecin). The observations were conducted by a team of one female and one male researcher and took place in public places that had posted an official recommendation to wear a face mask. Both researchers were medically experienced in physical signs of age and had to see the person and agree on the age-group classification, otherwise the person was excluded. An “incorrect fit” of face mask was defined as any deviant kind of mask use (i.e., covering only the mouth or the nose but not both, a loose fit forming gaps between the mask and the face, taking the mask off for coughing or sneezing). They considered all people in the public places as eligible except children under the estimated age of 10 years and individuals with visible physical disabilities. Ultimately, they observed 523 instances of incorrect mask use. Of these, 92 were of advanced age (60+ years), and 431 were not of advanced age (10-59 years).

Source: Linda Eckl and Stefan Hansch. “Gender- and age-related differences in misuse of face masks in COVID-19 prevention in central European cities.” medRXiv 2020.  Retrieved from: https://doi.org/10.1101/2020.11.11.20224030.

a.Your goal is to determine whether this outcome provides convincing evidence that of those who wear their face mask incorrectly, fewer are of advanced age (60+ years) than is expected by chance. Set up a simulation study to investigate this using the applet, and copy/paste your simulation setup below. Hint: Remember that this simulation should be set up to mimic what happens if a person who wears their face mask improperly is equally likely to be of advanced age as they are to be younger (i.e., you should be simulating results under the assumption that age is not related to whether the face mask is worn properly or not).  

b.Carry out a simulation study using the applet to determine whether this outcome provides evidence that of those who wear their face mask incorrectly, fewer are of advanced age (60+ years) than is expected by chance. In the end, you should have a graph showing the results of 1,000 runs of the simulation. Copy and paste this dot plot below.

Recall that of the 523 observed instances of incorrect mask use, 92 were of advanced age (60+ years). Write a paragraph to the researchers that summarizes (based on your simulation study) whether the data provide evidence that of those who wear their face mask incorrectly, fewer are of advanced age (60+ years) than is expected by chance.