Homework 1 (10 points)
STAT 110
Name(s) ___SOLUTION__________
Due: Thursday, January 31st by 4pm
1. 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®. 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)
There were 150 students in the study
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? You will use this value when setting up your spinner
proportions. (1 point)
P(graduate w/in 6 years) = 0.60
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. Copy and paste your results or provide a
detailed sketch below. (4 points)
Answers will vary
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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)
Since we’re trying to show the graduation rate is lower for student athletes,
fewer students graduating would be more extreme, i.e. less than 82.
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? (1 point)
Answers will vary, but you should have calculated
f.
# of dots at 82 or smaller
500
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)
If your p-value was less than 0.05 then you have evidence the graduation rate
is less for student athletes.
If your p-value was greater than 0.05 then you do not have evidence the
graduation rate is less for student athletes.
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