Table of contents

1. Intro to Stats and Collecting Data55m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically1h 45m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables2h 33m
6. Normal Distribution and Continuous Random Variables1h 38m
7. Sampling Distributions & Confidence Intervals: Mean1h 53m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample2h 19m
10. Hypothesis Testing for Two Samples3h 26m
11. Correlation1h 6m
12. Regression1h 35m
13. Chi-Square Tests & Goodness of Fit1h 57m
14. ANOVA1h 0m

9. Hypothesis Testing for One Sample

Steps in Hypothesis Testing

Statistics

9. Hypothesis Testing for One Sample

Steps in Hypothesis Testing

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2:34 minutes

Problem 11.1.1

Textbook Question

What is a nonparametric test? How does a nonparametric test differ from a parametric test? What are the advantages and disadvantages of using a nonparametric test?

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A nonparametric test is a type of statistical test that does not assume a specific distribution for the data (e.g., normal distribution). These tests are often used when the data does not meet the assumptions required for parametric tests, such as normality or homogeneity of variance.

Nonparametric tests differ from parametric tests in that parametric tests rely on assumptions about the population parameters (e.g., mean, variance) and the underlying distribution of the data. For example, a t-test assumes the data is normally distributed, while a nonparametric test like the Mann-Whitney U test does not make this assumption.

Advantages of nonparametric tests include their flexibility in handling data that is not normally distributed, their ability to work with ordinal data or data with outliers, and their applicability to small sample sizes. These features make them robust in situations where parametric tests may not be appropriate.

Disadvantages of nonparametric tests include lower statistical power compared to parametric tests when the assumptions of the parametric tests are met. This means that nonparametric tests may require larger sample sizes to detect the same effect size. Additionally, they may not provide as much detailed information about the data as parametric tests do.

In summary, nonparametric tests are useful tools for analyzing data that do not meet the assumptions of parametric tests. However, they should be used judiciously, considering the trade-offs in statistical power and the type of data being analyzed.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Nonparametric Tests

Nonparametric tests are statistical methods that do not assume a specific distribution for the data. They are often used when the data do not meet the assumptions required for parametric tests, such as normality or homogeneity of variance. Examples include the Mann-Whitney U test and the Kruskal-Wallis test, which are used for comparing medians rather than means.

Parametric Tests

Parametric tests are statistical tests that assume the data follows a certain distribution, typically a normal distribution. These tests, such as the t-test and ANOVA, rely on parameters like mean and standard deviation to make inferences about the population. They are generally more powerful than nonparametric tests when their assumptions are met, leading to more accurate results.

Advantages and Disadvantages

Nonparametric tests have the advantage of being applicable to a wider range of data types, including ordinal data and non-normally distributed interval data. They are also less sensitive to outliers. However, they may have less statistical power than parametric tests when the assumptions of the latter are satisfied, potentially leading to less precise estimates of effect sizes.

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In Exercises 7–12, find the critical value(s) and rejection region(s) for the type of chi-square test with sample size n and level of significance α.

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When the sign test is used, what population parameter is being tested?

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In Exercises 1–5, (a) identify the claim and state H0 and Ha, (b) decide which nonparametric test to use, (c) find the critical value(s), (d) find the test statistic, (e) decide whether to reject or fail to reject the null hypothesis, and (f) interpret the decision in the context of the original claim.

[APPLET] A meteorologist wants to determine whether days with rain occur randomly in April in his hometown. To do so, the meteorologist records whether it rains for each day in April. The results are shown, where R represents a day with rain and N represents a day with no rain. At , can the meteorologist conclude that days with rain are not random?

N R R N N N N R N R R N R R R

N R R R R N N N N R N R N N R

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