EXERCISES AND PROJECTS

Exercise 8-1

A professor at a small Midwestern college wishes to study the starting salaries of last year's class of 60 business administration and liberal arts majors. The data presented in the table below are to be used to complete Exercises 8-1, 8-2, and 8-3.

Name Starting Salary(in thousands of dollars) Major
Adkins 13.5 L (liberal arts)
Appleby 15.5 B (business administration)
Baldwin 17 B
Bennett 16 B
Brummett 14 L
Bullock 24 B
Carreway 14.5 L
Clements 21.5 B
Cooke 16.0 B
Davis 16.5 B
Dellinger 17 L
Dent 14.5 L
Derrick 18 B
Ellis 21 B
Farr 16 L
Foster 15 L
Furman 13 L
Garrett 15 B
Gehrig 15.5 L
Giles 9.5 L
Harris 15 B
Hayes 14.5 B
Higgs 13 B
Hooper 20 B
Jervis 15 L
Johnson 13.5 B
Jones 11 L
Kendrick 14 L
Knott 14 L
Lambert 18 B
Ledbetter 19 B
Lovedahl 12 B
McCall 14 B
Madison 15 B
Massey 14.5 B
Medlock 13 L
Moran 12 L
Mullins 15.5 B
Newell 16.5 B
Newton 15 B
O’Brien 14 B
Paschal 14 L
Petway 17.5 B
Pruitt 15.5 B
Ragsdale 21 B
Retton 13.5 L
Rogers 14 B
Sharpe 14.5 B
Smith 20 L
Sprouse 14.5 L
Stillwell 15 L
Taylor 16.5 B
Thompson 12.5 B
Tucker 15 L
Underwood 15.5 B
Vance 13 B
Waddell 16 B
Whitlock 13 L
Wood 16 B
Young 15.5 L

Mean starting salary: $15,400
Business administration majors: 36
Liberal arts majors: 24
  1. Using simple random sampling, select a sample of 10 persons. List the names of the persons you selected.
    1. ________________________________________________________________________
    2. ________________________________________________________________________
    3. ________________________________________________________________________
    4. ________________________________________________________________________
    5. ________________________________________________________________________
    6. ________________________________________________________________________
    7. ________________________________________________________________________
    8. ________________________________________________________________________
    9. ________________________________________________________________________
    10. ________________________________________________________________________
  2. Calculate the mean starting salary for your sample of 10 graduates. Mean starting salary: _______
  3. Using the mean you calculated for the sample above, calculate the mean starting salary for the population of 60 graduates.
    Estimated starting salary: _________
  4. Compare your estimated mean salary with the actual figure given at the bottom of the list of graduates. The difference between the actual mean salary and your estimate is the result of sampling error (assuming that you made no arithmetic errors).
    Sampling error = ____________
  5. What might you do to decrease the sampling error in this task?

Exercise 8-2

Using the list of graduates provided, select a systematic sample of 15 graduates. To begin, you must calculate your sampling interval (k) and then select a random number to start with. Indicate what these are in the spaces provided, then list the names of the 15 graduates selected for your sample.

  1. Sampling interval (k) = ________
  2. Start = ________
  3. Graduates selected:
    1. ___________
    2. ___________
    3. ___________
    4. ___________
    5. ___________
    6. ___________
    7. ___________
    8. ___________
    9. ___________
    10. ___________
    11. ___________
    12. ___________
    13. ___________
    14. ___________
    15. ___________
  4. Calculate the mean starting salary of the sample. Mean starting salary = ___________
  5. Use this statistic to estimate the mean starting salary of the total number of graduates.
    Estimated mean salary: ___________
  6. Compare this estimate with the actual starting salary given earlier to determine how much sampling error you have in this sample.
    Sampling error = ___________
  7. What might be done to decrease the amount of sampling error?

Exercise 8-3

Using the list of graduates provided, select a stratified sample of 15 graduates. The graduates are to be stratified by major (B = business administration, L = liberal arts).

  1. List below the names of the business administration majors you selected.
    1. _________________________________________________________________________________
    2. _________________________________________________________________________________
    3. _________________________________________________________________________________
    4. _________________________________________________________________________________
    5. _________________________________________________________________________________
    6. _________________________________________________________________________________
    7. _________________________________________________________________________________
    8. _________________________________________________________________________________
    9. _________________________________________________________________________________
    10. _________________________________________________________________________________
    11. _________________________________________________________________________________
    12. _________________________________________________________________________________
    13. _________________________________________________________________________________
    14. _________________________________________________________________________________
    15. _________________________________________________________________________________
  2. List below the names of the liberal arts majors you selected.
    1. _________________________________________________________________________________
    2. _________________________________________________________________________________
    3. _________________________________________________________________________________
    4. _________________________________________________________________________________
    5. _________________________________________________________________________________
    6. _________________________________________________________________________________
    7. _________________________________________________________________________________
    8. _________________________________________________________________________________
    9. _________________________________________________________________________________
    10. _________________________________________________________________________________
    11. _________________________________________________________________________________
    12. _________________________________________________________________________________
    13. _________________________________________________________________________________
    14. _________________________________________________________________________________
    15. _________________________________________________________________________________
  3. Calculate the mean starting salary of your sample: _________
  4. Estimate the starting salary for the population of graduates based on the sample mean.
    Estimated starting salary: ___________
  5. Compare the estimated starting salary with the actual starting salary to determine your sampling error:_
  6. Compare your sampling error in this sample with the error in an equal size sample (such as that selected for Exercise 8-2). How do they differ? Why do you suppose they differ?

Exercise 8-4

You want a sample of driver's license holders in Mellowberg, California, and the California Department of Motor Vehicles agrees to provide this sample data from a data tape that lists all current license holders. You want to estimate the number of years people have had their licenses. The standard deviation of this value in a population is .15, and you want the standard error of your estimate to be no larger than .012. Assuming there are 8,000 driver's license holders in Mellowberg, how big should your sample be?