Wiki Page, Math 13 - Perez Sandbox : Module 20 - Introduction to Hypothesis Testing (1a of 5)

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2026-01-17T21:15:29-08:00

Introduction

In inference, we use a sample to draw a conclusion about a population. Two types of inference are the focus of our work in this course.

Estimate a population parameter with a confidence interval.

Test a claim about a population parameter with a hypothesis test.

We can also use samples from two populations to compare those populations. In this situation, the two types of inference focus on differences in the parameters.

Estimate a difference in population parameters with a confidence interval.

Test a claim about a difference in population parameters with a hypothesis test.

Previously, we learned to estimate a population proportion using a confidence interval. For example, we estimated the proportion of all Tallahassee Community College students who are female and the proportion of all American adults who used the Internet to obtain medical information in the previous month. We will revisit confidence intervals in future modules.

Now we look more carefully at how to test a claim with a hypothesis test. Statistical investigations begin with research questions. We begin our discussion of hypothesis tests with research questions that require us to test a claim. Later we look at how a claim becomes a hypothesis.

EXAMPLE Research questions about testing claims

Here are some examples of research questions that include a claim about a population parameter or a claim about a relationship between two population parameters:

Is the average course load for community college students less than 12 semester hours?

This question contains a claim about a population mean.

The population is all community college students.

The variable is course load in semester hours. It is quantitative, so the parameter is a mean.

The claim is, “The mean course load for all community college students is less than 12 semester hours.”

Do the majority of community college students qualify for federal student loans?

This question contains a claim about a population proportion.

The population is all community college students.

The variable is Qualify for federal student loan (yes or no). It is categorical, so the parameter is a proportion.

The claim is, “The proportion of community college students who qualify is greater than 0.5” (a majority means more than half, or 0.5).

In community colleges, do female students and male students have different mean GPAs?

This question contains a claim that compares two population means.

The two populations are female community college students and male community college students.

The variable is GPA. It is quantitative, so the parameters are means.

The claim is, “The mean GPA for female community college students is different from the mean GPA for male community college students.”

Notice that the claim compares the two population means, but there is no claim about the numeric value of either mean.

Are college athletes more likely than non-athletes to receive academic advising?

This question contains a claim that compares two population proportions.

The populations are college athletes and college students who are not athletes.

The variable is Receive academic advising (yes or no).

The variable is categorical, so the parameters are proportions. The claim is, “The proportion of all college athletes who receive academic advising is greater than the proportion of all nonathletes in college who receive academic advising.”

Notice that the claim compares two population proportions, but there is no claim about the numeric value of either proportion.

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