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 throughout 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 or

- Submit joint answers, that you have both discussed, with up to one partner. (This does not need to be your week 1 partner.)

*If you decide to submit a single document
for 2 people:* 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 and Flip Introduction in Canvas

**2)** Below some graphs of answers to questions by the first 67 Stat 301 students to
complete the Initial Course Survey. Your task will be to identify which graph
belongs to which variable in the list below. 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)

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. Some of
these will be pure guesses, but provide a
justification for your choice based on the behavior of the graph.)

**3)** Early research has
found chimpanzees able to solve complex problems, like fitting sticks together
to make a rake to gather food. In a 1978 study published in *Science*,
Premack and Woodruff asked "To what extent does
the chimpanzee comprehend the elements of a problem situation and potential
solutions?" An adult chimpanzee (Sarah) was shown 30-second videotapes of
a human actor struggling with one of several problems (for example, not being
able to reach a banana, a record player not playing). Then Sarah was shown two
photographs, one that depicted a solution to the problem (like stepping on a
box vs. plugging in the record player) and one that did not.

The order in which the scenes were
presented to Sarah were randomized as was the left/right position of the photo
when presented to her. [Sarah had been raised since age one and had extensive
prior exposure to photographs and television.]
Researchers watched Sarah select one of the two photos, and they kept
track of whether Sarah chose the correct photo depicting a solution to the problem.
Of the eight scenarios shown to Sarah, she chose the correct photograph 7
times. Did she just get lucky or is this
convincing evidence that she can solve complex problems?

(a) Identify the observational units and
variable for this research question (e.g., Practice Problem A.B)

(b) Let represent Sarah’s probability of picking the
correct photograph. Provide a one-sentence interpretation of this probability
in context (e.g., Investigation B quiz, remember not to use words
like “chance”, “likelihood”, and “probability” in your interpretation of
probability), using the symbol to represent the unknown value.

(c) 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.

(d) Estimate the p-value for these results.
Include a screen capture of the applet displaying the inputs and the proportion
of repetitions output. Provide a one-sentence *interpretation* of this
p-value in context (e.g., Investigation B quiz). Note: We will
discuss hypotheses and p-values in Inv 1.2 Friday.

(e) Summarize the conclusions you would draw from
this study. Do you think Sarah got lucky or do you think something other than
random chance was at play? Be sure to justify your answer statistically!

*Extra Credit: *Explain why the “coin tossing model” may not be
appropriate for this study.

**Things to remember:**

·
*Right
skewed* distributions
have a longer right tail and *left skewed** *distributions have a longer left tail.
Don’t say a distribution is *even* when you mean symmetric; to me “even”
indicates flat rather than mound-shaped.

·
We
will use the symbol to refer to a “process probability.” Don’t
confuse this with the number from your math courses 😊.
We will report probabilities as decimals, not percentages. Balso be careful
saying "chance" or "likelihood" when you mean
"proportion" or "probability."

·
We
will differentiate between *evaluating* the p-value (do you think it’s
small) and *interpreting* the p-value (where I want the long-run relative
frequency interpretation). Any interpretations should also be in the context of
the research study (not just generic definitions).

·
If
we don't have evidence against the null hypothesis, the preferred phrasing is
"fail to reject the null hypothesis".
(Kinda like saying defendant is "not guilty" rather than
"proven innocent." Many statisticians bristle at the phrase "accept"
the null hypothesis because it sounds too much like "evidence for the null
hypothesis" or "we believe the null hypothesis with no doubt"