ANALYSIS OF STATISTICAL INFERENCE PROBLEMS PROPOSED IN THE UNIVERSITY ENTRANCE TEST IN ANDALUSIA
The most frequent difficulties described in research on statistical inference are the incorrect interpretation of the significance level, the incorrect definition of hypotheses, the confusion between statistical summaries and parameters, standardization errors and wrong determination of percentiles. Despite these difficulties, this topic is only included in the area of Mathematics Applied to Social Sciences for second year of high school students.
A factor that has a strong influence on the way that this subject is taught is the exam for entrance to university (EEU tests) that is used to evaluate the maturity of students who intend to enter the university in relation to the knowledge and skills they have developed during their high school studies. At the same time, these tests are also used to select students in certain careers and universities. Consequently, it is important to ensure that the contents of the test are directly related to those included in the high school curriculum.
Starting from these considerations, the goal of this work is to analyze the statistical inference problems appearing in the PAU tests within the subject Mathematics Applied to Social Sciences. These problems are one of the four that these students should solve in these tests and therefore a correct solution has an important weight on the final mark received by the students (and their likelihood to be able to follow their preferred studies).
We analyzed all the exams in Andalusia in June and September from 2003-2014 (six different exams each year), which represent a total of 144 problems of inference. Through a content analysis, we have firstly identified the different types of problems proposed that include: sample composition, applied distributions, sample mean distributions, probabilities calculation, confidence interval, estimation error, sample size or hypothesis testing. We also studied the probability distribution used (generally the uniform, normal, binomial or unspecified distributions) and the problem context within those included in the PISA tests.
We identified the categories for each variable with an inductive and cyclical procedure, by coding and analyzing the data to produce graphs and tables that helped us to draw conclusions about the distribution of these categories in each variable, its evolution with time and the problems potential difficulty. These results inform the teacher about the statistical knowledge that students need to pass the tests, and also allow us to identify criteria for improving the preparation of future evaluation tests.