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use the Kruskal - Wallis test. Clancy, Rowling, Tolstoy

Elementary Statistics | 12th Edition | ISBN: 9780321836960 | Authors: Mario F. Triola ISBN: 9780321836960 18

Solution for problem 6BSC Chapter 13.5

Elementary Statistics | 12th Edition

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Elementary Statistics | 12th Edition | ISBN: 9780321836960 | Authors: Mario F. Triola

Elementary Statistics | 12th Edition

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Problem 6BSC

use the Kruskal - Wallis test?. Clancy, Rowling, Tolstoy Readability? Pages were randomly selected by the author from ?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. The Flesch Reading Ease scores are listed on the next page. Use a 0.05 significance level to test die claim that the three samples are from populations with the same median. Do the books appear to have different reading levels of difficulty? Clancy 58.2?73.4?73.1?64.4?72.7?89.2?43.9?76.3?76.4?78.9?69.4?72.9 Rowling? 85.3?84.3?79.5?82.5?80.2?84.6?79.2?70.9?78.6?86.2?74.0?83.7 Tolstoy? 69.4?64.2?71.4?71.6?68.5?51.9?72.2?74.4?52.8?58.4?65.4?73.6

Step-by-Step Solution:

Solution 6BSC Step 1 Kruskal-Wallis test satisfies the following two requirements. 1. Sample data must be independent and drawn according to simple random sampling. 2. Each sample must contain minimum of five entries. By using the data from exercise, we see that the samples are drawn at random, where the three samples are independent to each other. Hence the first requirement is satisfied. Now, we see that the sample size of clancy is 12, sample size of Rowling is 12 and sample size of Tolstoy is 12. Hence the second requirement is satisfied. Therefore, the two requirements of Kruskal-Wallis test are satisfied. Step 2 By using = 0.05 level of significance we need t o test die claim that the three samples are from populations with the same median The Hypotheses can be expressed as H0 three samples are from populations with the same median H1 three samples are from populations with the different median All these three samples are combined together to get a big sample. We first order the absolute values of the difference scores and assign rank from 1 through ‘n’ to the smallest through largest absolute values of the difference scores, and assign the mean rank when there are ties in the absolute values of the difference scores. Clancy Rowling Tolstoy 58.2(4) 85.3(34) 69.4(10.5) 73.4(19) 84.3(32) 64.2(6) 73.1(18) 79.5(28) 71.4(13) 64.4(7) 82.5(30) 71.6(14) 72.7(16) 80.2(29) 68.5(9) 89.2(36) 84.6(33) 51.9(2) 43.9(1) 79.2(27) 72.2(15) 76.3(24) 70.9(12) 74.4(22) 76.4(25) 78.6(25) 52.8(3) 78.9(26) 86.2(35) 58.4(4) 69.4(10.5) 74(21) 65.4(8) 72.9(17) 83.7(31) 73.6(20) The smallest value is assigned as the rank 1, here 43.9 is the smallest value and so on up to the largest value 121.9 is assigned as rank 36.

Step 3 of 3

Chapter 13.5, Problem 6BSC is Solved
Textbook: Elementary Statistics
Edition: 12
Author: Mario F. Triola
ISBN: 9780321836960

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