Stat 301 – HW 1

Due noon, Friday, Jan. 10

The homework assignment below is to be submitted by noon on Friday. This does not mean wait until Thursday night to start! (You can bring a hard copy to class Thursday or to my office Friday (slide under my door), or upload into Canvas by Friday (If you upload your assignment, please upload separate files for problems 2, 3, and 4. You should also use Word or PDF format only.)

1) Initial course survey in PolyLearn

2) Below some variables (mostly answers to questions from Initial Course Survey for the first 50 respondents this quarter) 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.

· Heights of students in a past 301 class

· Number of siblings

· Number of states visited

· Political inclination (conservative, moderate, or liberal)

· Amount of change in pockets (dollar amount)

· Coke or Pepsi preference

· Mac or PC user

· Number of heads reported in 50 tosses of a coin

· Cost of last hair cut in a past 301 class

· Ratings of the value of statistics on a scale of (1)-(9)

(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.)

3) Reconsider what you learned about the definition of probability from the Investigation B. Use the same long-run relative frequency interpretation of probability to interpret what we mean by “probability” in the following (Hint: Don’t use the words probability, chance, or likelihood in your interpretation):

(a) The probability of getting a red M&M candy is .2. [Hint: For 20% of …. What happens? …]

(b) The probability of a four-of-a-kind in a five-card poker hand is 0.0240%.

(d) I heard that Clemson has a 53% chance of winning the game against LSU.

4) 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. Do his results provide strong evidence that Paul is doing something other than randomly guessing and perhaps has some psychic power?

(a) 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).

(b) If we let represent Paul’s probability of picking the winning team, what is the value of if Paul is randomly guessing?

(d) Use the One Proportion Inference applet to find a p-value. Include a copy of your computer results (e.g., screen capture) showing both the input values and the results.

(e) Interpret this p-value in the context of the study (what is it the probability of?)

(f) Based on your p-value, write out a conclusion in the context of the research question.

(g) 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.

(h) Do these data provide convincing evidence that Paul’s probability of picking the winning team is larger than 0.70? Justify your conclusion.

Possible Extension assignment entries

· Find another study of an animal used to predict outcomes of sporting events. Discuss the results.

· Attend Statistics job candidate talks and write a brief paragraph summarizing what you learned:

o Thursday 4:10-5:00 (38-136)

o Friday 11:10-12 (38-121)

o Monday 4:10-5:00 (35-209)

o Tuesday 11:10-12 (38-121)

· Post any helpful technology hints to the course discussion board