Stat 301 – HW 1

Due midnight, Friday, January 13

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 one-sentence 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 one-sentence interpretation of this p-value.

(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.)