Stat 2000, Section 001, Extra Credit (Due 4/26/2000 in class)

Each of the following questions is worth up to 20 points. The policy for extra credit is that final grades will be determined without looking at the extra credit points and cutoff point limits will be set. Only thereafter, extra credits will be added. Therefore, people that feel comfortable that they will be able to achieve the grade they are looking for through regular course work do not have to work on these extra credit questions. However, if you feel uncertain about the outcome of your final grade, you may want to work on one or multiple of these questions.

Please start each question on a new sheet. Extra credit will be awarded based on completeness and correctness of your answers.

1) We have seen several plots (e.g., the Weider empire) so far that provide only very little of the information one would like to have about the underlying topic. Can you find similar plots in newspapers, magazines, on the Web, or even in your textbooks? If so, then state questions you would like to have answered about the provided data but no such answers have been given in the plot, the accompanying caption or the main text where the plot is coming from. Indicate where the plot has been found and turn in a photocopy (or printout) of this plot and the accompanying text.
2) Statistical summaries at the federal (US) level show that Utah usually is ranked first in categories such as average number of children per married couple and ranked last in categories such as deaths due to lung cancer, drunk driving accidents, STD's, HIV, etc. A simple explanation for Utah's position in these rankings is the specific religious mix of Utah's population.
- a) Find any statistical data set on the Web that shows Utah's unique ranking (compared to other US states) that may be explained by the religious mix of its population. Indicate the source (i.e., URL) and provide a hardcopy of the data set.
- b) Find a source on the Web that lists the percentage of different religions for each of the 50 states. Indicate the source (i.e., URL) and provide a hardcopy of this data set. Is Utah's mix of religions unique for the US? Does any other state show a similar mix?
- c) For the data set you found in a), determine some of its characteristics, i.e., its mean, variance, etc. Assess graphically and numerically whether the data is approximately Normal distributed. Use a statistical software package (e.g., Excel or Statlets) to answer part c).
- d) Using your result from c), indicate whether the data value for Utah (from the data set you used in a) and c)) is significantly different from the data values for all other states. Explain all your steps that lead to your answer. It might be helpful to read Sections 6.2 and 7.1 in Moore/McCabe to answer part d).
3) Statistical data often is controversial. One such example is the wine consumption/heart attack data from Exercise 2.5 in Moore/McCabe.

In addition to parts a) through c) from the book, answer the following questions:
- d) Calculate the least squares regression line and the correlation coefficient r.
- e) If you were a doctor, would you recommend to your patients to drink some wine? Answer this question only from the statistical point of view, using the results from a) through d) above.
- f) At this stage in Stat 2000, we all should be a bit suspicious about the results we get from a) through d) and the conclusion drawn in e). Isn't there a way how we might even strengthen the hypothesis that wine consumption reduces heart attacks? List at least two countries that might be possible candidates to strengthen the hypothesis and indicate why you think these countries might be possible candidates.. The following Web site might be of some help:
  http://intowine.com/
- g) Now that we found two candidate countries that might support the hypothesis, which additional information do we need for these countries?
- h) If we want to weaken the hypothesis that wine consumption reduces heart attacks, which criteria must a country fulfill such that it weakens the hypothesis? There are two different scenarios how this can happen.
- i) Now you have to do some speculation - list two countries for which you would like to get additional information such that these countries weaken the hypothesis. Explain why you speculated that these two countries might be possible candidates.
- j) Can you find recent data on wine consumption and heart attacks for those countries listed in Moore/McCabe and the countries you listed in g) and i)? Indicate the URLs where this data is located and include a printout of the data for our countries.
- k) Also read about the "French Paradox" at
  http://www.intowine.com/health.html
  and
  http://intowine.com/healthap.html.
  
  If you were a doctor, would you now recommend to your patients to drink some wine? Answer this question only from the statistical point of view, now using the results from a) through j) above.
- l) If you were a doctor and recommended to your patients to drink some wine from the statistical point of view, you are done now. If you did not make the recommendation to drink some wine, you still have to explain to your patients that know about the original study that wine drinking does not cause a lower heart disease death rate but instead, that wine drinking is associated with some other factors that may cause a lower heart disease death rate. Which are these other factors? And how are they associated to wine drinking?
4) This question is similar to Assignment 10, Exercise 3. All parts of this question are based on the following probability density function (pdf):
- a) Sketch a graph of f(x).
- b) Verify that f(x) is a pdf.
- c) Calculate the cumulative distribution function (cdf) F(x).
- d) Sketch a graph of F(x). Recalling the rules for a cdf, this part d) will allow you to check your result of part c).
- e) Indicate P(X < 0.5), P(X < 1.8), P(X < 2.9), and P(X < 3.5).
5) There will be a fifth question posted in about 10 days (with a later due date) that contains exercises from Moore/McCabe on material that will be discussed in class during the last week, but won't be part of the last regular Assignment 13.