University of Central Florida (UCF) QMB3200 Quantitative Business Tools II Midterm Practice Exam

A common assumption of the t-test is that samples are selected randomly. Random sampling is crucial because it helps ensure that the samples are representative of the population from which they are drawn, minimizing bias and allowing for valid inferences to be made about the population based on sample data. This assumption supports the validity of the statistical tests applied to the samples and underpins many statistical techniques.

The other assumptions of the t-test often include the requirement that the data should ideally be normally distributed, particularly if the sample size is small. However, if the sample size is large enough, the Central Limit Theorem indicates that the distribution of sample means will approximate normality, regardless of the shape of the distribution of the population. Additionally, the dependent variable in a t-test is typically continuous, not categorical, and the sizes of the two samples being compared do not need to be equal, although some variations of the t-test can handle unequal sample sizes. Thus, the assumption of random sampling is fundamental and aligns well with the overall principles of statistical analysis.