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 22m
11. Correlation1h 6m
12. Regression1h 4m
13. Chi-Square Tests & Goodness of Fit1h 20m
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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2:02 minutes

Problem 13.5.3

Textbook Question

Notation For the data given in Exercise 1, identify the values of n1, n2, n3 and N.

Verified step by step guidance

Step 1: Understand the problem. The question asks to identify the values of n1, n2, n3, and N. Here, n1, n2, and n3 represent the sample sizes of three different groups or categories, and N represents the total sample size, which is the sum of all individual sample sizes.

Step 2: Review the data provided in Exercise 1. Locate the sample sizes for each group (n1, n2, n3) in the dataset. These values are typically given as counts or frequencies for each group.

Step 3: Assign the values of n1, n2, and n3 based on the data. For example, if the first group has 10 observations, n1 = 10. Repeat this for the second and third groups to find n2 and n3.

Step 4: Calculate the total sample size, N, by summing up the individual sample sizes. Use the formula:

N = n_{1} + n_{2} + n_{3}

Step 5: Verify your calculations to ensure accuracy. Double-check the values of n1, n2, n3, and N to confirm they align with the data provided in Exercise 1.

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Key Concepts

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

Sample Size (n)

In statistics, the sample size (n) refers to the number of observations or data points collected from a population for analysis. It is crucial for determining the reliability and validity of statistical inferences. Different groups may have different sample sizes, denoted as n1, n2, n3, etc., depending on how the data is segmented.

Total Sample Size (N)

The total sample size (N) is the sum of all individual sample sizes from different groups. It represents the overall number of observations used in a study and is important for calculating various statistical measures, such as means and variances. Understanding N helps in assessing the power of statistical tests and the generalizability of results.

Data Segmentation

Data segmentation involves dividing a dataset into distinct groups based on specific criteria, such as demographics or experimental conditions. This process allows for more detailed analysis and comparison between groups. Identifying values like n1, n2, and n3 is essential for understanding how the data is structured and how different segments contribute to the overall findings.

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Textbook Question

Heights of Females from ANSUR I and ANSUR II Example 1 in this section used samples of heights of males from Data Set 1 “ANSUR I 1988” and Data Set 2 “ANSUR II 2012.” Listed below are samples of heights (mm) of females from those same data sets. Are the requirements for using the Wilcoxon rank-sum test satisfied? Why or why not?

Textbook Question

Rank Sum After ranking the combined list of female heights given in Exercise 1, find the sum of the ranks for the ANSUR I sample.

Textbook Question

What Are We Testing? Refer to the sample data in Exercise 1. Assuming that we use the Wilcoxon rank-sum test with those data, identify the null hypothesis and all possible alternative hypotheses.

Textbook Question

Requirements Assume that we want to use the data from Exercise 1 with the Kruskal-Wallis test. Are the requirements satisfied? Explain.

Textbook Question

HIC Measurements Listed below are head injury criterion (HIC) measurements from crash tests of small, midsize, large, and SUV vehicles. In using the Kruskal-Wallis test, we must rank all of the data combined, and then we must find the sum of the ranks for each sample. Find the sum of the ranks for each of the four samples.

Textbook Question

Using the Kruskal-Wallis Test

In Exercises 5–8, use the Kruskal-Wallis test.

HIC Measurements Use the sample data from Exercise 1 with a 0.05 significance level to test the claim that small, midsize, large, and SUV vehicles have the same median HIC measurement in car crash tests.

Textbook Question

Arsenic in Rice Listed below are amounts of arsenic in samples of brown rice from three different states. The amounts are in micrograms of arsenic and all samples have the same serving size. The data are from the Food and Drug Administration. Use a 0.01 significance level to test the claim that the three samples are from populations with the same median.

Textbook Question

Clancy, Rowling, and Tolstoy Ease of Reading Pages were randomly selected from three books: The Bear and the Dragon by Tom Clancy, Harry Potter and the Sorcerer’s Stone by J. K. Rowling, and War and Peace by Leo Tolstoy. Listed below are Flesch Reading Ease Scores for those pages. Higher scores correspond to pages that are easier to read. Use a 0.01 significance level to test the claim that pages from books by those three authors have the same median Flesch Reading Ease score.

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