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9: Hypothesis Testing with One Sample

Last updated

Mar 17, 2025
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- 8.12: Solutions
- 9.0: Introduction to Hypothesis Testing

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9.0: Introduction to Hypothesis Testing
This page emphasizes the significance of hypothesis development and testing within the scientific method, highlighting its origins in theories and logical reasoning. It contrasts empirical validation with authority-based knowledge and illustrates practical applications in evaluating claims, such as in consumer behavior and business assertions. The chapter aims to equip readers with skills in hypothesis testing for means and proportions while understanding associated errors.
9.1: Null and Alternative Hypotheses
The actual test begins by considering two hypotheses. They are called the null hypothesis and the alternative hypothesis. These hypotheses contain opposing viewpoints.
9.2: Outcomes and the Type I and Type II Errors
This page covers hypothesis testing, focusing on the null hypothesis $H_0$ and its associated errors: Type I (incorrectly rejecting a true $H_0$ ) and Type II (failing to reject a false $H_0$ ). It highlights the importance of minimizing Type I errors ( $\alpha$ ) and discusses their significance in real-world contexts, such as claims by It's a Boy Genetic Labs and monitoring "red tide" toxins.
9.3: One-Sample Test
This page covers hypothesis testing for population means and proportions, detailing the use of normal and Student's $t$ -distributions, calculation of test statistics (Z-values), and decision-making based on critical values and p-values. It emphasizes the bias towards the null hypothesis, discusses one-tailed and two-tailed tests, and outlines a systematic approach for hypothesis testing, including the importance of sample size and the appropriate distribution based on known standard deviation.
9.4: Full Hypothesis Test Examples
This page discusses hypothesis testing through various examples, including swimming times, sales performance, and machine fluid filling. It covers one-tailed and two-tailed tests, null and alternative hypotheses, and significance levels. Key findings indicate improved swimming speed with goggles, high sales performance, and under-filling by a machine.
9.5: Key Terms
This page explains essential statistical concepts such as binomial distribution, central limit theorem, confidence interval, and hypothesis testing. It highlights the importance of terms like normal distribution, standard deviation, and error types in understanding statistical sampling and decision-making processes. Each concept is contextualized to illustrate its relevance in statistics and probability.
9.6: Chapter Review
This page explains null and alternative hypotheses in hypothesis testing, highlighting the significance of Type I and Type II errors. It clarifies that the null hypothesis (H0) represents equality, while the alternative hypothesis (Ha) indicates inequality. The text emphasizes the importance of statistical power and the conditions for testing populations with t-tests or normal tests, based on sample size and distribution.
9.7: Formula Review
This page discusses hypothesis testing test statistics, highlighting differences based on sample size and knowledge of population standard deviation. It explains that for sample sizes under 30, specific formulas are used based on standard deviation knowledge, while for sizes over 30, the Z-statistic is consistently applied. The page also includes information on the test statistic formula for proportions.
9.8: Practice
This page covers hypothesis testing, detailing null and alternative hypotheses, random variables, and associated errors like Type I and II. It includes examples related to Internet speed, average salaries, and sociological claims, as well as questions on specific hypotheses and applicable distributions. The importance of sample size and standard deviation in choosing testing methods (left-tailed, right-tailed, two-tailed) is also emphasized.
9.9: Homework
This page covers statistical hypothesis testing, discussing null and alternative hypotheses across various scenarios such as retirement working years, voting statistics, and salary comparisons. It highlights Type I and Type II errors, examines specific cases like employee sick days and smoking rates, and emphasizes processes for conducting hypothesis tests.
9.10: References
This page outlines various sources of data for hypothesis testing, including organizations such as the National Institute of Mental Health and the CDC, along with studies on public health, education, crime, and demographics. It provides links to relevant publications, which aid in formulating null and alternative hypotheses in research.
9.11: Solutions
This page discusses statistical hypothesis tests, including left-tailed, right-tailed, and two-tailed tests, addressing null and alternative hypotheses and associated errors. It analyzes student solutions where they reject the null hypothesis about nurses' salaries and stock ownership but not for natural gas heating.

Curated and edited by Kristin Kuter | Saint Mary's College, Notre Dame, IN

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