Hypothesis Testing with One Sample

7. Hypothesis Testing with One Sample#

This chapter explores the essential concepts and methods of hypothesis testing, a fundamental aspect of statistical inference. Students will learn a systematic approach to making inferences about population parameters based on sample data. Starting with the formulation of null and alternative hypotheses, the chapter covers key elements of hypothesis testing, such as the interpretation of Type I and Type II errors, differences between one-tailed and two-tailed tests, and the role of critical values and p-values in decision-making.

Later sections focus on practical applications, including hypothesis testing for population means with both known and unknown standard deviations, as well as tests for population proportions. These topics equip students with the knowledge to apply hypothesis testing in diverse real-world scenarios, supporting data-driven decision-making across disciplines.

Chapter Outline:

  1. Introduction: An overview of hypothesis testing and its role in statistical inference.

  2. Null and Alternative Hypotheses: Formulating null and alternative hypotheses for testing population parameters.

  3. Outcomes and Type I and Type II Errors: Understanding possible outcomes and the implications of Type I and Type II errors in hypothesis testing.

  4. One-Tail, Two-Tail Tests, and Critical Values: Differentiating between one-tailed and two-tailed tests, and the use of critical values in hypothesis testing.

  5. P-Value: Introducing the concept of p-values and their role in determining statistical significance.

  6. Hypothesis Testing of a Single Mean: The process of testing hypotheses about a single population mean.

  7. Hypothesis Tests for One Population Mean When σ Is Known: Conducting hypothesis tests with known population standard deviation.

  8. Hypothesis Tests for One Population Mean When σ Is Unknown: Applying hypothesis testing when the population standard deviation is unknown, using the t-distribution.

  9. Hypothesis Testing of a Single Proportion: Techniques for hypothesis testing involving population proportions.

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