8: Hypothesis Testing with One Sample

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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.

8.1: Prelude to Hypothesis Testing
This page covers hypothesis testing, highlighting the distinction between Type I and Type II errors. It guides students through the testing process for single population means and proportions, emphasizing the use of sample data to make population inferences. The chapter details formulating hypotheses, data collection, distribution selection, data analysis, and conclusion drawing, while introducing key concepts like hypothesis testing and confidence intervals.
8.2: Hypothesis Testing for One Population
This page covers fundamental concepts in hypothesis testing in statistics, including the definitions and significance of null (H₀) and alternative hypotheses (H₁). It explains Type I and Type II errors, their probabilities ($\alpha$ and $\beta$), and the importance of minimizing these errors. The page discusses hypothesis testing methods utilizing p-values, the significance level, and the decision-making process based on these metrics.
8.3: Hypothesis Tests for Means with Known Population Standard Deviation
This page covers hypothesis testing for population parameters, including mean, proportion, and standard deviation, utilizing the z-distribution. It details both Traditional and p-value methods for hypothesis testing and presents a case study on Jeffrey's swimming times, where a p-value of 0.0187 supports rejecting the null hypothesis. It also discusses Type I and Type II errors and provides examples and exercises.
8.4: Hypothesis Tests for Means with Unknown Population Standard Deviation
This page covers statistical tools for analyzing population parameters, including the mean, proportion, and standard deviation, with a focus on hypothesis testing using the Student's t-distribution when the population standard deviation is unknown. It compares traditional and p-value methods for hypothesis testing, emphasizing the role of power and sample size.
8.5: Hypothesis Tests for Proportions
This page discusses hypothesis testing for population proportions using z-tests, covering critical components such as normal approximations and binomial conditions. It outlines Traditional and p-value methods, including hypothesis setup, statistic calculation, and decision-making based on critical values or p-values, illustrated through examples.
8.E: Hypothesis Testing (Optional Exercises)

Contributors and Attributions

Barbara Illowsky and Susan Dean (De Anza College) with many other contributing authors. Content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at http://cnx.org/contents/30189442-699...b91b9de@18.114.

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