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)
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)
http://www.statlets.com/statletsindex.htm,
determine the following for the full "Cost of Victories" data set, i.e., for all n = 30 teams: (7 Points)
- a) Mean Wins, Mean Payroll.
- b) Variance of Wins, Variance of Payroll.
- c) Histogram for Wins, Histogram for Payroll.
- d) Draw a scatterplot and calculate the least squares regression line, where x = Payroll and y = Wins.
- e) Residual plot of e's vs. x's.
Note that the data has been stored in electronic form at
http://www.math.usu.edu/~symanzik/teaching/2000_stat2000/victories.dat.
The Payroll has been rounded to the nearest million.
Please provide printouts from all your graphics and numerical results. Copy numerical reults into a text file and print them from there. To print graphics from a Java applet, either use the print screen option of your computer or capture the portion of the screen that contains the graphics through a screen grabber such as SnagIt which may be downloaded for free from TechSmith Corporation's web site at
http://www.techsmith.com.
If a feature is not supported by this software package, please indicate so.
Please provide printouts from all your graphics and numerical results. (7 Points)