Stat 2000, Section 001, Homework Assignment 9 (15 Points)

(3/27/2017 - Due Friday 4/7/2017 by 10:20am)

• 0) Reading: Sections 5.1
  
  
• 1) Please work on the following textbook exercises in Moore/McCabe/Craig:
  
  
  • Exercise 4.109, 4.110, 4.111, 4.131, 4.134, 4.135, 4.141, 4.144, 4.145, 4.149, 5.7, 5.8, 5.12, 5.14, 5.24, 5.28
    
    For all your calculations, show your work!
    
    
• 2) Bayes' Rule:
  There is a 10% chance that a student is sick on a homework due day. Nevertheless, 5% of the students who are sick still manage to turn in their homework. 80% of the students who are not sick turn in their homework. What is
  
  P(student sick | student does not turn in homework) ?
  
  To answer this question, sketch a tree diagram, properly name the events, and then apply Bayes' Rule. Show your work!
  
  
• 3) The Sampling Distribution of a Sample Mean in StatCrunch:
  
  • Load the file
    http://www.math.usu.edu/~symanzik/teaching/2017_stat2000/Population_FPP_StatCrunch.csv
    into StatCrunch. We already explored the variables "Pop1" and "Pop2" in class. "Pop3" will be explored in the recitation lectures. You have to deal only with variables "Pop4" and "Pop5" in this question.
    
  • First draw the histograms for these two variables. For the bins, set "start at" to "-0.05" and "width" to "0.1". Add markers for the mean and the median. At the bottom of the menu, indiate to use the same x-axis and y-axis and increase "columns per page" to 2. Save the resulting two histograms and submit as part of your answer. Describe the shape of both histograms and compare mean and median. Use the proper statistical terms.
    
  • Next, draw 1000 samples of size 10 from "Pop4" and compute the mean for each sample (use `mean("Sample(Pop4)")' in the proper text field). Repeat for 1000 samples of size 50, and repeat once more for 1000 samples of size 100.
    
  • Then, do exactly the same for "Pop5".
    
  • As your last two steps, you have to create histograms, QQ plots, and numerical summaries of these sample outcomes: For the bins of the histograms, set "start at" to "0" and "width" to "0.025". Add markers for the mean and the median. At the bottom of the menu, indiate to use the same x-axis and y-axis and increase "rows per page" to 2 and "columns per page" to 3. Save the resulting six histograms and submit as part of your answer. Describe the shape of the six histograms and compare mean and median. Use the proper statistical terms. Does any of these histograms approximate a Normal distribution? Which one(s)? Also look at the QQ plots and use them to determine whether a particular set of samples is approximately Normal distributed. So, which sample sizes would be sufficient to argue that the sampling distribution of the sample mean is approximately Normal for "Pop4" and "Pop5", respectively?
    
  • Finally, create the numerical summaries of these sample outcomes (and submit as part of your answer) and compare with those from "Pop4" and "Pop5". How do the means of the sample means relate to the population means? Use the proper statistical term. And how do the standard deviations of the sample means relate to the population standard deviation? Based on the population standard deviation, what should the standard deviations of the sample means be, based on the formula from Section 5.1? Are we close to these theoretical values or not?