Sections 2.6.1‑4 How the Standard Normal Distribution Leads to Hypothesis Testing

Supplementary Resource Materials

(ways to test hypotheses about a population based on your sample data)

• The Theoretical Basis for Inferential Statistical Methods
  • The Logic of Statistical Inference (Ray Cooksey)

• The Standard Normal Distribution and Single Sample Hypothesis Testing

  Hypothesis Tests about One Mean $\mu $ (variance ${{\sigma }^{2}}$ known)

  • Single Sample Hypothesis z‑test: Part 1 (Brandon Foltz)
  • Single Sample Hypothesis z‑test: Part 2 (Brandon Foltz)
  • Single Sample Hypothesis z‑test: Part 3 (Brandon Foltz)
  • Introduction to z‑Tests for One Mean (sigma σ known) (jbstatistics)
  • z‑Tests for One Mean: an example (jbstatistics)

  The $p$‑value approach

  • What is a p‑value (for a Hypothesis Test)? (jbstatistics)
  • A Tool for Visualizing the p‑value for Various Hypothesis Tests (statdistributions.com)
  • z‑Tests for One Mean (p‑value approach) (jbstatistics)
  • Statistical Significance versus Practical Significance (jbstatistics)

  The critical‑value approach

  • z‑Tests for One Mean (rejection region or critical value approach) (jbstatistics)

  Hypothesis Tests about One Proportion $p$ (large sample)

  • An Introduction to Inference for One Proportion (jbstatistics)
  • Inference for One Proportion: An Example (jbstatistics)
  • Inference for One Proportion: An example for a Confidence Interval and a Hypothesis Test (jbstatistics)

Reference Materials

(Questions to consider when you are reading/writing a report containing the results of a single sample hypothesis test)

• What hypotheses are being tested? Are the hypotheses about a population mean, a population proportion, or some other population characteristic?
• Was the appropriate test used? Does the validity of the test depend on any assumptions about the sample or about the population from which the sample was selected? If so, are the assumptions reasonable?
• What is the $p$‑value associated with the test? Was a significance level reported (as opposed to simply reporting the $p$‑value)? Is the chosen significance level reasonable?
• Are the conclusions drawn consistent with the results of the hypothesis test?
  (Introduction to Statistics & Data Analysis by Peck, Olsen & Devore, Cengage Learning, 2014, p. 549)