The Effects of Data Distribution on the Confidence Interval of the Number of Projected Items

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