Setting a question paper for test, quiz, and examination is one of the teachers’ tasks. The factors that are usually taken into consideration in carrying out this particular task are the level of difficulty of the questions and the level of the students’ ability. In addition, teachers will also have to consider the number of questions that have impact on the examination. This research describes a model-based test theory to study the confidence intervals for the projected number of items of a test, given the reliability of the test, the difficulty of the question, and the students’ ability. Using the simulated data, the confidence intervals of the projected number of items were examined. The probability coverage and the length of the confidence interval were also used to evaluate the confidence intervals. The results showed that the data with a normal distribution, the ratio variance components of 4:1:5 and reliability equal to 0.80 gave the best confidence interval for the projected number of items.
The classical procedures of comparing two groups, such as t-test are, usually restricted with the assumptions of normality and equal variances. When these assumptions are violated, the rates of the Type I errors of the independent samples t-test are affected, particularly when the sample sizes are small. In this situation, the bootstrap procedure has an advantage over the parametric t-test. In this study, the performances of the bootstrap procedure and the independent sample t-test were investigated. The investigation focused on the power of both the test procedures to compare the two groups under different design specifications for normal and chi-square distributions. The results showed that the bootstrap procedure has a slight edge over the conventional t-test in term of the rate of achieving the benchmark level for both the distributions. In fact, the bootstrap procedure consistently outperformed the conventional t-test across all the combinations of the test conditions.