Supplementary Exercise 3.74 of IPS7e ------------------------------------ The short answer to the question is that with a larger sample size, the results from the study are going to be more precise. We will in Lecture 5 encounter a rule for the precision of estimates, expressing that the precision increases with sample size (as one would intuitively expect). In order to elaborate a bit on what the precision of estimates means, it is helpful to consider the entire statistical setup. The population of interest appears to be students attending college, perhaps at a specific university or more generally. The questions being about part-time work, there is definitely a need to define the targeted population, because one could easily imagine large differences in the answers from different groups of students (say by sociodemographic group). Each question will have its answers distributed in a certain way across the entire distribution. The distribution of answers we achieve from a sample of size 25 (or 100) is not going to match the distribution in the population exactly, but we would expect a better match with a larger sample size. In particular, we would expect a sample estimate (such as a mean or a proportion) to be closer to the corresponding value from the population with a larger sample size. We saw one example of this in Exercise 4.9 (with simulated data). Whether a sample size of 25 (or 100) is adequate, is a difficult question that cannot be answered meaningfully without more information about the objective of the study and some assumptions about the distribution in the population. We will get to statistical sample size calculations later in the course.