Homework 1 (20 points)
STAT 110
Name(s) _______________________________
Due: Monday, September 10th by 4pm
1. A colleague from Winona State University conducted a survey to explore computer preference
of Winona State undergraduate students (age 18 – 24). My colleague was interested in
determining whether students preferred a Mac or a PC. The survey was taken by 468 randomly
selected students and 244 of the 468 students surveyed reported that they prefer using a Mac.
a. Define the population of interest. (1 point)
b. Define the sample. (1 point)
c. Identify the variable of interest. (1 point)
2. Suppose a study was conducted to explore cola preference of Winona State University
undergraduate students (age 18 – 24). There were 75 randomly selected students who made
blinded evaluations of pairs of cola drinks: Coke and Pepsi. The order of the drinks was
randomized for each student, and after tasting both each student indicated which cola they
preferred.
In this scenario if students really have no cola preference, cola choice can be mimicked by
flipping a coin resulting in a 50/50 chance of picking either Coke or Pepsi. A simulation study
was carried out using Tinkerplots 2®. The scenario was repeated 100 times, and each time the
number of students who chose Pepsi was recorded. The dotplot below shows the results from
the 100 trials.
a. What does each dot in the plot represent? (1 point)
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b. Since WSU is a Pepsi campus, it is believed that the majority of students prefer Pepsi. In
the study, 45 out of the 75 (60%) students chose Pepsi. What outcomes (other than 45)
would have convinced you even more that the majority of all students at WSU prefer
Pepsi? We say these outcomes are even more extreme than the observed data.
(1 point)
c. What proportion of the simulated outcomes is at least as extreme as the observed
result? In other words, if the students had no preference and were simply picking a cola
at random, what is the probability that we would observe 45 or more who picked Pepsi?
Estimate this probability from the dotplot above. (2 points)
d. For the population that this sample represents, do the observed data present strong
evidence that the majority of WSU students prefer Pepsi? Explain. Hint: You’ll want to
use your answer from part c in your explanation. (2 points)
3. The National Collegiate Athletic Association (NCAA) measures academic outcomes of studentathletes with the Graduation Success Rate (GSR) system – the percentage of eligible athletes
who graduate within six years of entering college. It is well known that the GSR for all students
at Division I colleges is 60%. A random sample of 150 student-athletes from Division I colleges
was taken and it was found that 82 of them graduated within six years of entering college.
Research Question –
Is there evidence that student-athletes are less likely to graduate within six years
of entering college?
To investigate this research question, you will need to carry out a simulation study in Tinkerplots
2 ®. You will simulate this experiment in order to see what outcomes are likely (or unlikely) to
occur if the GSR for student-athletes is the same as it is for all students at Division I colleges.
You should keep the following things in mind when designing the simulation study.
a. How many subjects are in this study? You will use this when setting the Repeat value.
(1 point)
b. Each trial has two possible outcomes: the student-athlete graduated within six years of
entering college or the student-athlete did not graduate within six years of entering
college. What is the probability a randomly selected student-athlete will graduate from
college within six years of entering college if the graduation rate is the same for all
students at Division I colleges? (1 point)
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c. Carry out the rest of the simulation like we’ve done in class. In the end, you should have
a graph showing the results of 500 trials. Provide a detailed sketch of your results
below. (4 points)
d. Recall that in the actual study 82 of the 150 student-athletes graduated within six years
of entering college. What outcomes (other than 82) would have convinced you even
more that student-athletes are less likely to graduate within six years of entering
college? (1 point)
e. What proportion of the simulated outcomes is at least as extreme as the observed data?
In other words, if the GSR for student-athletes is the same as all students at Division I
colleges, what is the probability (from the above dotplot) of observing what we did or
something more extreme? (2 points)
f.
Do the data provide evidence that the GSR for student-athletes is lower than all
students at Division I colleges? Explain. Hint: You’ll want to use your answer from part
e in your explanation. (2 points)
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