Stat 250, Section 003, Homework Assignment 12 (Due 4/28/99 in class)

• 1) Please work on the following textbook exercises in Moore:
  
  
  • Exercise 4.42, 4.44, 4.46, 4.47, 4.48, 4.50 (2 points each)
    
  
  
  
• 2) In Quiz 3, Question 1, Part 3, several students suggested an approach that is different from my solution to conduct a simple random sample (SRS).
  
  Variant 1: Use the random digits table B and assume that the 2-digit numbers represent the age (we pretend that we know the ages of all blood donors in our population of size 40). If a 2-digit random number represents a valid age that exists in the population, we include the first person of this age into our sample. If the same 2-digit random number occurs again, we include the second person of this age into our sample. For example, in our population, the age 37 occurs three times, the age 23 occurs two times, etc. On the first occurrance of a 37 in the random digit table, the first person of age 37 will be included. On the second orrurrance the second person. We continue until we have a sample of size n.
  
  Variant 2: Similar to Variant 1. However, if an age occurs more then once in our population, we would use another random digit to randomly select the person among all persons that are of the same previously determined age. The person selected in this 2-step procedure will be included into our sample. We continue until we have a sample of size n.
  
  Starting at line 101, we would end up with ages 19 (not in population), 22 (include this person), 39 (include this person), 50 (include this person), 34 (include this person), etc.
  
  The big question now is - which of these variants represent a simple random sample? Explain! To support your reasoning, you should assume that we just have a population of size 3 of ages 22, 37, and 37, i.e., person 1: 22, person 2: 37, and person 3: 37. We are interested in a SRS of size 2. Indicate the probabilities to end up with a sample that contains persons 1 & 2, persons 1 & 3, or persons 2 & 3 under Variant 1 and Variant 2, respectively. So, which variant represents a SRS? (5 points)
  
  
• 3) In Quiz 3, Question 1, Part 6, what is the chance to end up with individuals 05, 20, 07, 37, and 13 (according to my ordering in the solutions) in a SRS of size 5 out of a population of 40. And what is the chance to end up with individuals 05, 20, 07, 37, and 15 in a SRS of size 5 out of this same population?
  
  As we have seen, a minimum mean age of 22 years is impossible. Based on your answers above, how likely is an outcome of an average age of 23.2 years? (3 points)