Exercises

  1. Set the criterion for being selected (using the black bar) to about 60. What is the mean score for students who are selected? What is the mean score for students who are not selected? Why are more than half the students selected?
  2. Is the mean true score for selected students greater than 60? Why or why not?
  3. For selected students, is the mean score on Test 1 higher than the mean true score? Why or why not?
  4. What percent of the selected students were lucky on Test 1(they guessed right on more than half the questions they did not know)? Why is it higher than 50%?
  5. As a whole, were selected students luckier on Test 1 or Test 2? Why?
  6. Did selected students score better on Test 1 or Test 2? Why?
  7. What is closer to the mean of all students, the mean true score of selected students or the mean Test 1 score of selected students? Which is closer to the mean Test 2 score of selected students?
  8. Which is higher, the mean Test 2 score of selected students or the mean Test 2 score of non-selected students? Why?
  9. What is the effect of the strictness of the selection criterion on the percentage of selected students that are lucky? Why?
  10. How does the strictness of the criterion affect the difference between the mean scores on Tests 1 and 2 of the selected students?
  11. How does the standard deviation of the true scores affect the correlation between Test 1 and Test 2 scores? Explain why.