Explanation Calculation: The given data represents the sample of 15 students rakings on midterm and final examinations in statistics course. The formula for Spearman rank- correlation coefficient is given as follows: r s = 1 − 6 ∑ d 2 n ( n 2 − 1 ) . Here, ∑ d 2 is the sum of squares of the differences of the ranks of the data set and n is the sample size. The value of ∑ d 2 can be obtained as follows: Midterm Final d d 2 1 4 –3 9 2 7 –5 25 3 1 2 4 4 3 1 1 5 8 –3 9 6 2 4 16 7 5 2 4 8 12 –4 16 9 6 3 9 10 9 1 1 11 14 –3 9 12 15 –3 9 13 11 2 4 14 10 4 16 15 13 2 4 ∑ d 2 = 136 Substitute n as 15 and ∑ d 2 as 136 in above formula, r s = 1 − 6 × 136 15 ( 15 2 − 1 ) = 1 − 816 15 ( 225 − 1 ) = 1 − 816 15 × 224 = 1 − 816 3 , 360 = 1 − 0.243 = 0.757 Hence, the Spearman rank-correlation coefficient is 0.757. The population rank correlation is denoted as ρ s . Here, the claim is that “there exist a significant positive rank correlation between the two exams”. State the hypotheses: Null hypothesis: H 0 : ρ s = 0 Alternative hypothesis: H a : ρ s ≠ 0 The formula for the significant rank correlation is given as follows: σ r s = 1 n − 1

Modern Business Statistics with Microsoft Excel (MindTap Course List)

5th Edition

ISBN: 9781285433301

Author: David R. Anderson, Dennis J. Sweeney, Thomas A. Williams

Publisher: Cengage Learning

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Question

Chapter 18, Problem 46SE

To determine

Find the Spearman rank-correlation coefficient and test for a significant correlation with α=0.10.

Find the p-value and make conclusion.

Expert Solution & Answer

Chapter 18 Solutions

Modern Business Statistics with Microsoft Excel (MindTap Course List)

Ch. 18.1 - 1. The following hypothesis test is to be...Ch. 18.1 - 2. Ten individuals participated in a taste test...Ch. 18.1 - 3. The median number of part-time employees at...Ch. 18.1 - 4. Net assets for the 50 largest stock mutual...Ch. 18.1 - Prob. 5E Ch. 18.1 - Prob. 6E Ch. 18.1 - Prob. 7E Ch. 18.1 - Prob. 8E Ch. 18.1 - Prob. 9E Ch. 18.1 - Prob. 10E

Ch. 18.1 - Prob. 11E Ch. 18.2 - 12. Two fuel additives are tested to determine...Ch. 18.2 - 13. A sample of 10 men was used in a study to test...Ch. 18.2 - Percents of on-time arrivals for flights in 2006...Ch. 18.2 - Prob. 15E Ch. 18.2 - Prob. 16E Ch. 18.2 - Prob. 17E Ch. 18.3 - Two fuel additives are being tested to determine...Ch. 18.3 - Samples of starting annual salaries for...Ch. 18.3 - The gap between the earnings of men and women with...Ch. 18.3 - Prob. 21E Ch. 18.3 - Prob. 22E Ch. 18.3 - Police records show the following numbers of daily...Ch. 18.3 - A certain brand of microwave oven was priced at 10...Ch. 18.3 - Prob. 25E Ch. 18.4 - A sample of 15 consumers provided the following...Ch. 18.4 - Three admission test preparation programs are...Ch. 18.4 - Prob. 28E Ch. 18.4 - Prob. 29E Ch. 18.4 - A large corporation sends many of its first-level...Ch. 18.4 - Prob. 31E Ch. 18.5 - Prob. 32E Ch. 18.5 - 33. Consider the following two sets of rankings...Ch. 18.5 - Prob. 34E Ch. 18.5 - Prob. 35E Ch. 18.5 - 36. The rankings of a sample of professional...Ch. 18.5 - Prob. 37E Ch. 18 - 38. A survey asked the following question: Do you...Ch. 18 - Prob. 39SE Ch. 18 - Prob. 40SE Ch. 18 - Prob. 41SE Ch. 18 - Prob. 42SE Ch. 18 - Prob. 43SE Ch. 18 - Prob. 44SE Ch. 18 - Prob. 45SE Ch. 18 - Prob. 46SE Ch. 18 - Prob. 47SE

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Find the Spearman rank- correlation coefficient and test for a significant correlation with α = 0.10 . Find the p -value and make conclusion.

Solution Summary: The author analyzes the Spearman rank-correlation coefficient and the p-value of the correlation between the two exams.

Find the Spearman rank-correlation coefficient and test for a significant correlation with α=0.10.

Find the p-value and make conclusion.

Chapter 18 Solutions

Find the Spearman rank- correlation coefficient and test for a significant correlation with α = 0.10 . Find the p -value and make conclusion.

Solution Summary: The author analyzes the Spearman rank-correlation coefficient and the p-value of the correlation between the two exams.

Find the Spearman rank-correlation coefficient and test for a significant correlation with α=0.10. Find the p-value and make conclusion.

Chapter 18 Solutions

Find the Spearman rank-correlation coefficient and test for a significant correlation with α=0.10.

Find the p-value and make conclusion.