Stat 2000, Section 001, Homework Assignment 3 (30 Points)

(1/27/2012 - Due Friday 2/3/2012 by 9:35am)

• 0) Reading: Section 1.3
  
  
• 1) Please work on the following textbook exercises in Moore/McCabe/Craig:
  
  
  • Exercise 1.82 (2 points), 1.97 (2), 1.116 (2), 1.117 (2), 1.118 (1), 1.119 (1), 1.121 (2), 1.122 (2), 1.126 (2), 1.127 (2)
    
    
• 2) First read the text between Exercises 1.131 and 1.132. Then work on the following textbook exercises in Moore/McCabe/Craig:
  
  
  • Exercise 1.132, 1.133, 1.134, 1.135, 1.136, 1.138, 1.140 (1 point each)
    
    
• 3) Standard Deviation (5 points):
  Revisit the "Standard Deviation" applet at http://www.math.usu.edu/~schneit/CTIS/SD/. Increase the number of columns to 20.
  
  Note that Moore/McCabe/Craig state on p41: "Many calculators offer a choice between dividing by n and dividing by n-1, ...". When we divide by n-1, we call this the "sample standard deviation" (or just "standard deviation") and we work with this SD in most cases in Stat 2000. When we divide by n, we call this the "population standard deviation". Note that this applet calculates the "population standard deviation" and not our "sample standard deviation"!
  
  Create the following plots and include printouts, screendumps, or photos of your results:
  
  (a) A plot that consists of exactly 2 observations where the "population standard deviation" is exactly 1.0. Turn on "Show values".
  
  (b) Create 2 more plots where the "population standard deviation" is exactly 1.0, but now use 4 and 6 observations. Can you describe additional plots where the "population standard deviation" also will be 1.0? No need to produce such plots - just describe them.
  
  (c) Calculate the exact "sample standard deviations" for for your three previous plots (for 2, 4, and 6 observations). Show your calculations. Note that all of your values are whole numbers in the range from 1 to 20 (as you were asked to increase the number of columns to 20).
  
  (d) When we place one observation each at 7, 8, 9, 10, 11, 12, and 13, we obtain a mean of 10.0 and a "population standard deviation" of exactly 2.0. Where do we have to add an observation to obtain a "sample standard deviation" of exactly 2.0? Verify your guess, either by hand calculations by doing the calculations in CrunchIt or any other software. Hint: What changes automatically in our calculations when we flip from the "population standard deviation" to the "sample standard deviation" -- and what needs to remain the same as before (and how can we achieve this?)?
  
  
• 4) Recitation Problems (RPs): The following RPs will be discussed during the recitation lectures next week:
  
  Exercise 1.123, 1.137, 1.139, 1.141, 1.142, 1,144, 1.145, 1.146, 1.147
  
  Please refer to hw01.html for additional information regarding the RPs.