Module 8: Inference for One Proportion
Hypothesis Testing (1 of 5)
Hypothesis Testing (1 of 5)
Learning OUTCOMES
- When testing a claim, distinguish among situations involving one population mean, one population proportion, two population means, or two population proportions.
- Given a claim about a population, determine null and alternative hypotheses.
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.
In “Estimating a Population Proportion,” 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
Let’s revisit some of the research questions from examples in the module Types of Statistical Studies and Producing Data that involve testing a claim.
Is the average course load for community college students less than 12 semester hours? This question contains a claim about a population mean. The question contains information about the population, the variable, and the parameter. 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 and information about the population, the variable, and the parameter. 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. Again, we see informa