Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What information is derived from random samples of a given size?

1. Basic Statistics

2. Experimental Outcomes

3. Sampling Distribution of the Mean

4. Control Variables

The correct answer is: Sampling Distribution of the Mean

When taking random samples of a given size, the resulting information leads to the concept of the Sampling Distribution of the Mean. This distribution describes how the means of these random samples would behave if you were to take an infinite number of samples of that size from the same population. The Central Limit Theorem plays a key role here, as it states that as the sample size increases, the sampling distribution of the mean tends to follow a normal distribution, regardless of the original population's distribution, given that the sample size is sufficiently large (typically n ≥ 30 is considered sufficient). This understanding is critical for inferential statistics, where we make predictions or generalizations about a population based on sample data. For instance, it helps in estimating population parameters and conducting hypothesis testing, ensuring that the conclusions drawn from sample data are statistically valid. In contrast, while Basic Statistics might involve summarizing data or calculating averages, it does not specifically encompass the behavior and characteristics of means from random samples. Experimental Outcomes refer to results from conducting experiments rather than information derived from sampling distributions. Control Variables are factors kept constant to ensure that an experiment tests only the effects of the independent variable, which is also not directly relevant to sampling distributions.