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Hypothesis Testing of Single Mean and Single Proportion: Introduction

Module by: Susan Dean, Dr. Barbara Illowsky

Student Learning Objectives

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

The 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 the data supports the claim that is made about the population.

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 support one of the hypotheses.
  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

Confidential Interval:
An interval estimate for unknown population parameter. This depends on:
  • The desired confidence level.
  • What is known for the distribution information (for ex., known variance).
  • Gathering from the sampling information.
Hypothesis Testing:
Based on sample evidence 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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