For this unit, you should determine (individually or in pairs) a survey question which has three alternatives which can be ranked in terms of preference. Submit your question to me on or before Wednesday, February 7. I will put all of the questions together and survey both sections of the course on Friday. By Monday, Feb. 12, I will give you the ordinal ballot for your question. With that information, you should:
Determine the plurality winner (or the plurality opinion, in the case of an opinion question).
Determine the winner according to Borda's method.
Determine the winner according to Hare's method.
Determine if there is a Condorcet winner.
Discuss your results. If the winner differs according to various social choice methods, which one would you choose as the winner? Justify your answer.
Your project will be evaluated primarily according to the accuracy of your results. You should include your survey question and a table showing the ordinal ballot, and all work involved in determining the winner according to various methods. For an A or B, your conclusions and discussion should be well written and presented in a professional style.
A pharmaceutical manufacturer forms tablets by compressing a granular material that contains the active ingredient and various fillers. The hardness of a sample from each lot of tablets is measured in order to control the compression process. The target values for the hardness are =11.5 and =0.2. To monitor the process, random samples of 4 tablets are taken twenty times a day. The data below shows the results of the control process for three successive days. Data Set A shows the samples from the first day, Data Set B contains samples from the second day, etc. Each value in the table represents the mean hardness measurement from 4 tablets.
Part 1:
Construct a three separate control charts - one for each day. Each chart should clearly show the upper and lower control limits, as well as data points for the twenty samples.
Part 2:
Based on the guidelines we discussed in class, analyze each of your control charts. Do you have evidence of points which are out of control? Is there other evidence that should cause concern to the manufacturer? On the days, if any, when the process appears to have a problem, does the chart suggest a gradual shift in the mean, or a sudden change in the production process? Give a reason for your analysis.
The purpose of this project is for you to show your understanding of how descriptive and inferential statistics might be used to explore questions surrounding the public health concern of polio in the United States in the middle of the twentieth century. On Monday, April 23, you will see a 30-minute video which is condensed from the PBS documentary: A Paralyzing Fear: The Story of Polio in America. The video (both the condensed and unedited, 90-min. version) are available on reserve in the library under my name. As you watch the story of the history of polio and its treatment, consider the following questions:
What are some ways in which descriptive statistics might have been used to gain a sense of where polio epidemics were occurring and the common characteristics of its victims?
At first, public health officials responded to polio in the same way they reduced the spread of other diseases, by improving sanitation and concentrating on possible sources of contamination (flies, stray cats, immigrant populations, etc.) Describe a specific statistical study which could have been carried out and might have disproved one of these theories.
What are some possible variables (in pairs) that may have had a significant linear correlation? Name at least two. Looking back now, would you expect your examples to have a positive or negative correlation?
To determine if the Salk or Sabin vaccine was effective, statisticians had to vaccinate a sample of 200,000 children with the vaccine and give another 200,000 a placebo injection. In this process, how could confidence intervals have been helpful in determining if the vaccine was effective?
In the vaccine testing, why was a placebo necessary? Why not simply vaccinate all 400,000 children in the study and observe the results?
What are the advantages of statistical analysis of a public health concern such as the polio epidemics, as opposed to simple trial and error and observation?
Your assignment is to answer the above questions in a short paper (more than one page, fewer than 5), in which you discuss specifically how the statistical tools we have discussed in chapters 5, 6, and 8 might be used to provide reliable answers to the questions posed. Your project will be based on 30 points, of which 5 points will be reserved for spelling/grammatical quality. Your paper should be typed and one-sided.
For this project, you should begin by visiting the website
and reading the article you find there, titled "Toward a Fairer Expansion Draft", by Ivars Peterson.
The context of this article is that two new teams are to be created, with owners who will choose the teams from a pool of available talent. The author begins by describing how these new teams are typically drafted, and the disadvantage of these methods. Discuss these methods and why they can be unfair.
The draft protocol that Dawson suggests is based on the ‘Divide and Choose' technique that we discussed in class. Why factors make the expansion draft too complex for the standard divide and choose division procedure? Discuss at least three of these factors.
In your own words, describe the protocol that Dawson suggests. (You should not answer this with a verbatim quote from the article's description.)
Do you think it is likely that major sports leagues will adopt Dawson's protocol? Why or why not?
For your project, write a brief paper in which you answer the above questions, in complete sentences and preferably in paragraph form.