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

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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.

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Chapter 18 Solutions

STATISTICS F/BUSINESS+ECONOMICS-TEXT

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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.