Stat 301 – HW 1

Due midnight, Friday, January 12

 

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)

 

A graph with blue dots

Description automatically generated

 

(b)

A graph with blue dots

Description automatically generated

 

(c)

A line with blue dots

Description automatically generated

 

(d)

A graph with blue dots

Description automatically generated

 

(e)

A graph with blue dots

Description automatically generated

 

(f)

A graph with blue dots

Description automatically generated

 

(g)

A line of blue dots

Description automatically generated

 

(h)

A blue dots on a white background

Description automatically generated

 

(i)

A white background with black text

Description automatically generated

 

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.

A collage of a person in a suit

Description automatically generated

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"