The homework assignment below is to be submitted in Canvas. The official deadline is Friday night but Saturday submissions will be graded without penalty. You are expected to be working on the assignment through the week, especially asking questions in class on Friday. Please upload separate files for problems 2 and 3, and use Word or PDF format only.
You are encouraged
to work together on the assignment, but then you should:

Write up your own
answers

Submit joint answers,
that you have both discussed, with one partner.
If you decide to
submit a single document: In Canvas, you need to join a HW1 group before you
submit. To do this: click on the People link on the left panel. Then select the
Groups tab. You can search on HW 1. Find
an empty group and have both of you join the group. Then submit the assignment.
Only one group member should submit the assignment but both names need to be
inside the file. If you submit the assignment
individually, just submit. You can change
your groups for different assignments.
1) Initial course survey in Canvas
2) Below some variables (mostly answers to questions by 57 Stat 301 students on a
previous Initial Course Survey) and some graphs. Your task will be to identify
which graph belongs to which variable. You will be graded on your justification
more than the correctness of your matches.
1.
Heights
of students
2.
Number
of siblings
3.
Number
of states visited
4.
Political
inclination (conservative, moderate, or liberal)
5.
Amount
of change in pockets (dollar amount)
6.
Coke or
Pepsi preference
7.
Mac or
PC user
8.
Number
of heads recorded when asked to toss a coin 50 times
9.
Cost of
last hair cut
10. Ratings of the value of statistics on a scale
of (1)(9)
(Make sure you are seeing the entire image!)
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
Write
a paragraph explaining how you decided which graph belonged with which
variable. (You can cite “process of elimination”
for at most one graph but should give justifications for the others, clearly
state any assumptions you make along the way. For example, you might consider
whether reasonable numerical values can be placed along the horizontal axis as
well as what shape you expect the distribution to have. Be sure you offer
conjectures to choose between graphs of similar shape.)
3) People
use animals to predict outcomes of sporting events and elections mostly by
having the animals pick between two containers of food, each representing one
of the two teams or the two candidates involved. Probably the most famous of
these is Paul the Octopus from Germany who was correct in all eight of his
predictions for the 2010 World Cup (Nov
2022 article). Do Paul’s results provide strong evidence that he was doing
doing something other than randomly guessing and perhaps ha some psychic power?
(a) Let represent Paul’s probability of picking the
winning team. Provide a onesentence interpretation of this probability, using
the symbol to represent the unknown value.
(b) Can we use a “coin tossing” simulation
to represent the scenario where Paul is simply guessing? Explain
(and discuss any limitations you see in using this model to represent Paul’s
behavior).
(c) If we let represent Paul’s probability of picking the
winning team, what is the value of if Paul was randomly guessing? If Paul
had some psychic power, what does this imply about the value of ?
(d) Use the One Proportion
Inference applet to generate a distribution for the number of correct picks in 8
attempts for guessing. Include a copy of your computer
results (e.g., screen capture)
showing both the input values and the results.
(e) Based on your
graph, does 8 correct identifications in 8 attempts appear to be surprising for
a guessing octopus?
(f) Next we will
learn that the calculated probability of 8 correct identifications in 8
attempts for a guessing octopus is 0.0039. Provide a onesentence interpretation
of this pvalue.
(g) For the 2008
Euro games, Paul made 4 out of 6 correct predictions. Create an appropriate graph to represent the
performance you would expect to see if Paul was simply guessing? Include your graph. Based
on your graph, does Paul’s performance provide strong evidence that he had
psychic power for the Euro games?
(h)
As was stated earlier, many animals are used to predict outcomes of sporting
events with most of them not doing any better than random chance and therefore
not getting much publicity. Paul made the news because he was so accurate. Do
you think it is surprising that some animal would be very successful like Paul
was? Explain. (What about the individual correct predictions cited in the
above article.)