| Tag | Value |
|---|---|
| file | Reliability_eur-reliability-206-en_eur-reliability-206-en |
| name | eur-reliability-206-en |
| section | Reliability/Analysis/Cronbach's alpha |
| type | schoice |
| solution | TRUE, FALSE, FALSE, FALSE |
| Type | Conceptual |
| Program | |
| Language | English |
| Level | Statistical Reasoning |
Students who didn’t pass the exam (X1) of a social psychology course at the University of Amsterdam have to take a retest (X2) two weeks after the first exam. The criterion to pass and the difficulty level are equal for the exam and the retest. The reliability of the exam is 1 and the reliability of the retest is 0. Suppose that the students do not prepare for the retest, so their true scores are equal on the exam and the retest. Assume that in the population, 30% of the students have a true score above the criterion. Assume furthermore that the probability of passing based on chance alone is 50% for both tests. What is the probability that a student who has to take the retest, has a true score above the criterion, so 𝑝(𝜏 ≥ 𝑐𝑟𝑖𝑡|𝑋2 = 1)?
The answer is 0. The reliability of the first exam is 1, so everybody with a true score equal to or higher than the criterion passes the first exam and will not take the retest. Everybody who takes the retest therefore has a true score below the criterion.