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Hypothesis Testing: Single Mean and Single Proportion

Module by: Susan Dean, Barbara Illowsky, Ph.D.. E-mail the authors

Student Learning Outcomes

By the end of this chapter, the student should be able to:

  • Differentiate between Type I and Type II Errors
  • Describe hypothesis testing in general and in practice
  • Conduct and interpret hypothesis tests for a single population mean, population standard deviation known.
  • Conduct and interpret hypothesis tests for a single population mean, population standard deviation unknown.
  • Conduct and interpret hypothesis tests for a single population proportion.

Introduction

One job of a statistician is to make statistical inferences about populations based on samples taken from the population. Confidence intervals are one way to estimate a population parameter. Another way to make a statistical inference is to make a decision about a parameter. For instance, a car dealer advertises that its new small truck gets 35 miles per gallon, on the average. A tutoring service claims that its method of tutoring helps 90% of its students get an A or a B. A company says that women managers in their company earn an average of $60,000 per year.

A statistician will make a decision about these claims. This process is called "hypothesis testing." A hypothesis test involves collecting data from a sample and evaluating the data. Then, the statistician makes a decision as to whether or not there is sufficient evidence based upon analyses of the data, to reject the null hypothesis.

In this chapter, you will conduct hypothesis tests on single means and single proportions. You will also learn about the errors associated with these tests.

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

  1. Set up two contradictory hypotheses.
  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 sample data by performing the calculations that ultimately will allow you to reject or fail to reject the null hypothesis.
  5. Make a decision and write a meaningful conclusion.

Note:

To do the hypothesis test homework problems for this chapter and later chapters, make copies of the appropriate special solution sheets. See the Table of Contents topic "Solution Sheets".

Glossary

Confidence Interval (CI):
An interval estimate for an unknown population parameter. This depends on:
  • The desired confidence level.
  • Information that is known about the distribution (for example, known standard deviation).
  • The sample and its size.
Hypothesis Testing:
Based on sample evidence, a procedure to determine whether the hypothesis stated is a reasonable statement and cannot be rejected, or is unreasonable and should be rejected.

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