Stat 2000, Section 001, Homework Assignment 6 (30 Points)

(2/24/2012 - Due Friday 3/2/2012 by 9:35am)

• 0) Reading: Section 3.1
  
  
• 1) Please work on the following textbook exercises in Moore/McCabe/Craig:
  
  
  • Exercise 2.135 (2 points), 2.140 (2), 2.142 (2), 2.175 (2), 3.17 (2), 3.18 (2), 3.19 (2), 3.25 (2), 3.27 (1), 3.28 (1), 3.30 (2), 3.32 (2), 3.35 (2), 3.46 (1)
    
    
• 2) Simpson's Paradox (5 points):
  Revisit the "Simpson's Paradox" applet at http://www.math.usu.edu/~schneit/CTIS/SP/. In the "Data Menu", select the "Berkeley Admissions" data set. These data have been extensively discussed in the literature, see for example the section called the "Berkeley gender bias case" at http://en.wikipedia.org/wiki/Simpson's_paradox. Note that numbers from Departments A & B have been combined into the "Easy" component and numbers from Departments C to F have been combined into the "Hard" component in the applet (and wikipedia seems to list an incorrect number as the number of male applicants in Department F typically is listed as 373 and not as 272).
  
  Based on the applet, answer the following questions:
  
  (a) If 0% of women and 0% of men would apply to harder admittance majors, what would be the overall percentage of men and the overall percentage of women that would be admitted? Is Simpson's Paradox observed in this situation?
  
  (b) If 100% of women and 100% of men would apply to harder admittance majors, what would be the overall percentage of men and the overall percentage of women that would be admitted? Is Simpson's Paradox observed in this situation?
  
  (c) If 75% of women and 25% of men would apply to harder admittance majors, what would be the overall percentage of men and the overall percentage of women that would be admitted? Is Simpson's Paradox observed in this situation?
  
  (d) If 60% of women would apply to harder admittance majors, about what percentage of men would have to apply to the harder admittance majors so that Simpson's Paradox barely is observed. You should narrow this percentage down to a 1%-interval, say between 8% to 9% or between 92% and 93% (just giving two incorrect answers here).
  
  (e) If 15% of men would apply to harder admittance majors, about what percentage of women would have to apply to the harder admittance majors so that Simpson's Paradox barely is observed. You should narrow this percentage down to a 1%-interval, say between 8% to 9% or between 92% and 93% (just giving two incorrect answers here).
  
  
• 3) Recitation Problems (RPs):
  Please work on the following textbook exercises in Moore/McCabe/Craig:
  
  
  • Exercise 3.37, 3.38, 3.42, 3.45
    
    
  Please refer to hw01.html for additional information regarding the RPs.