To construct: The Box-and-whisker plot for each region and check whether the median annual incomes appear to differ between regions. To perform: The Wilcoxon rank sum test to test the claim that the median annual incomes in the Northeast and South are the same. To perform: The Kruskal-Wallis test and test the claim that the distributions of annual incomes for all four regions are the same. To Perform: A one-way ANOVA test and test the claim that the average annual incomes for all four regions are the same and compare the result with Kruskal-Wallis test.

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Answer 1

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Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

Chapter 11, Problem 6T

To determine

To construct: The Box-and-whisker plot for each region and check whether the median annual incomes appear to differ between regions.

To perform: The Wilcoxon rank sum test to test the claim that the median annual incomes in the Northeast and South are the same.

To perform: The Kruskal-Wallis test and test the claim that the distributions of annual incomes for all four regions are the same.

To Perform: A one-way ANOVA test and test the claim that the average annual incomes for all four regions are the same and compare the result with Kruskal-Wallis test.

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1- Let A = {A1, A2, ...), in which A, A, = 0, when i j. a) Is A a π-system? If not, which element(s) should be added to A to become a π-system? b) Prove that σ(A) consists of the finite or countable unions of elements of A; i.c., A E σ(A) if and only if there exists finite or countable sequence {n} such that A = U₁An (Hint: Let F be such class; prove that F is a σ-filed containing A.) c) Let p ≥ 0 be a sequence of non-negative real numbers with Σip₁ = 1. Using p₁'s, how do you construct a probability measure on σ(A)? (Hint: use extension theorem.) 2- Construct an example for which P(lim sup A,) = 1 and P(lim inf An) = 0.

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Answer 2

Question

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

Chapter 11, Problem 6T

To determine

To construct: The Box-and-whisker plot for each region and check whether the median annual incomes appear to differ between regions.

To perform: The Wilcoxon rank sum test to test the claim that the median annual incomes in the Northeast and South are the same.

To perform: The Kruskal-Wallis test and test the claim that the distributions of annual incomes for all four regions are the same.

To Perform: A one-way ANOVA test and test the claim that the average annual incomes for all four regions are the same and compare the result with Kruskal-Wallis test.

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 3

Question

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

Chapter 11, Problem 6T

To determine

To construct: The Box-and-whisker plot for each region and check whether the median annual incomes appear to differ between regions.

To perform: The Wilcoxon rank sum test to test the claim that the median annual incomes in the Northeast and South are the same.

To perform: The Kruskal-Wallis test and test the claim that the distributions of annual incomes for all four regions are the same.

To Perform: A one-way ANOVA test and test the claim that the average annual incomes for all four regions are the same and compare the result with Kruskal-Wallis test.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Question

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

Chapter 11, Problem 6T

To determine