Section outline

  • A Dalmation wearing a red color, appears to be in a nature setting, and there is a spout of water from a water fountain.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 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 decline to reject the null hypothesis.
    5. Make a decision and write a meaningful conclusion.

    Image Caption: You can use a hypothesis test to decide if a dog breeder’s claim that every Dalmatian has 35 spots is statistically sound. (Credit: Robert Neff)

    (Content & Image Source: Chapter 9 Introduction, Introductory Statistics, Barbara Illowsky and Susan Dean, OpenStax, CC BY 4.0 License)
    Upon completion of this module, you will be able to: 

    8.1 Null and Alternative Hypotheses
    • Describe hypothesis testing in general and in practice.
    8.2 Outcomes and the Type I and Type II Errors
    • Differentiate between Type I and Type II errors in a hypothesis test.
    8.3 Distribution Needed for Hypothesis Testing
    • Identify the distribution required to conduct a hypothesis test.
    8.4 Rare Events, the Sample, Decision and Conclusion
    • Identify rare events
    • Conduct and interpret hypothesis tests.
    • Describe a decision and conclusion.
    8.5 Additional Information and Full Hypothesis Test Examples
    • 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.

    To achieve these objectives:
    1. Read the Module 9 Introduction (see above).
    2. Read Sections 8.1 - 8.5 of Chapter 8: Hypothesis Testing with One Sample in Introductory Statistics (links to each Section provided below)
    3. Complete the MyOpenMath Homework Assignments for the topics in the Chapter (links provided below) - These are graded!
    4. View the Chapter 8 Review (link provided below)
    5. Practice the problems in the Chapter 8 Practice and Homework, checking the solutions provided (links to each provided below)
    6. Submit the Chapter 8 Project: Hypothesis Testing of a Single Mean and Single Proportion (links to project and submission link provided below)
    7. Complete the MyOpenMath Quiz for Chapter 8 (link provided below) - This is graded!
    8. Once you complete the Quiz, upload your work in the Quiz Work Upload Assignment using the submission link below.
    9. Post in the Chapter 8 Q&A Discussion Forum - link provided below.

    Note the check boxes to the right that help you track your progress: some are automatic, and some are manual.

    Module Pressbooks Resources and Activities

    You will find the following resources and activities in this module at the Pressbooks website. Click on the links below to access or complete each item.

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