Hypothesis Tests for Single Population Parameters

One of the jobs a statistician frequently performs is to make statistical inferences about populations based on samples taken from the population. The confidence intervals we learned about in the previous chapter are one way to estimate a population parameter. Another way to make a statistical inference is to make a true or false decision about a population parameter.

For example, suppose a car dealer advertises that its new small truck gets an average of [latex]15[/latex] kilometres per litre. As a consumer, can we believe this claim? Or suppose a tutoring service claims that its method of tutoring helps [latex]90\%[/latex] of its students get an A or a B. Should parents believe this claim? What if a company says that women managers in their company earn an average of [latex]\$60,000[/latex] per year? How could we test the validity of these claims?

A statistician will make a decision, based on sound statistical analysis, about whether such claims about a population parameter are true or false. This process is called hypothesis testing. A hypothesis test involves collecting data from a sample, evaluating the data, and using the evidence provided by the sample data to make a decision about whether or not there is sufficient evidence to reject or not reject the null hypothesis.

Hypothesis testing consists of two contradictory hypotheses: a decision based on the data and a conclusion. To perform a hypothesis test, a statistician will:

1. Set up two contradictory hypotheses. Only one of these hypotheses is true, and the hypothesis test will determine which of the hypotheses is most likely true.
2. Collect sample data. (In homework problems, the data or summary statistics will be given to you.)
3. Determine the correct distribution to perform the hypothesis test.
4. Analyze the sample data by performing calculations that ultimately will allow you to reject or not reject the null hypothesis.
5. Make a decision and write a meaningful conclusion.

This chapter will focus on the hypothesis test process, how to conduct hypothesis tests on single population means and single population proportions, and errors associated with hypothesis testing. In later chapters, we will learn how to conduct a hypothesis test on other population parameters, including population variance, two population means, two population proportions, and two population variances.

“8.1 Introduction to Hypothesis Testing” from Introduction to Statistics by Valerie Watts is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.