Wiki Page, Math 13 - Perez Sandbox : Module 17 - Distribution of Sample Proportions (1 of 6)

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2026-01-17T21:15:20-08:00

Introduction

In this module we will work with categorical variables, so the statistics and the parameters will be proportions. Later in the course we will work with quantitative variables, so the statistics and parameters will be means.

In the Big Picture, we see that inference is based on probability. In this module, we begin the process of developing a probability model to describe the long-run behavior of proportions from random samples.

EXAMPLE Gender in the population of part-time college students

According to a 2010 report from the American Council on Education, females make up 57% of the U.S. college population. With the rising costs of education and a poor economy, many students are working more and attending college part time. We anticipate that if we look at the population of part-time college students, a larger percentage will be female. Let’s say we predict that 60% of part-time college students are female.

We don’t have information about the population of part-time college students, so we select a random sample of 25 part-time college students and calculate the proportion of the sample that is female. We don’t expect the sample proportion to be exactly 0.60. So, how much could the sample proportion vary from 0.60 for us to feel confident in our prediction?

To answer this question, we need to understand how much sample proportions will vary if the parameter is 0.60. We investigate this in the next activity.

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