a. Explanation Given info: The evaluation score for two consecutive years was given. Calculation : The formula for r is obtained below: r = S S x y S S x x S S y y Where, S S x x = ∑ x i 2 − ( ∑ x i ) 2 n S S x y = ∑ x i y i − ∑ x i ∑ y i n S S x x = ∑ y i 2 − ( ∑ y i ) 2 n The table represents the measurements required for calculating the correlation coefficient r : Year 1 ( x ) Year 2 ( y ) x 2 y 2 x y 55 53 3,025 2,809 2,915 53 51 2,809 2,601 2,703 51 51 2,601 2,601 2,601 39 34 1,521 1,156 1,326 37 36 1,369 1,296 1,332 37 35 1,369 1,225 1,295 37 30 1,369 900 1,110 35 37 1,225 1,369 1,295 35 35 1,225 1,225 1,225 34 40 1,156 1,600 1,360 33 35 1,089 1,225 1,155 33 36 1,089 1,296 1,188 33 33 1,089 1,089 1,089 32 42 1,024 1,764 1,344 32 36 1,024 1,296 1,152 32 31 1,024 961 992 32 32 1,024 1,024 1,024 31 34 9,1 1,156 1,054 31 30 961 900 930 31 31 961 961 961 31 50 961 2,500 1,550 27 28 729 784 756 22 31 484 961 682 17 32 289 1,024 544 ∑ x = 830 ∑ y = 883 ∑ x 2 = 30 , 378 ∑ y 2 = 33 , 723 ∑ x y = 31 , 583 Substitute the values ∑ x b. To determine To test : Whether there is any sufficient evidence of a positive linear relationship between year 2 PARS score ( y ) and year 1 PARS score ( x ) or not.

13th Edition

ISBN: 9780134596839

Author: MCCLAVE

Publisher: PEARSON

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Chapter 11.5, Problem 11.78ACI

To determine

To obtain: The correlation coefficient r and interpret the results.

To determine

To test: Whether there is any sufficient evidence of a positive linear relationship between year 2 PARS score (y) and year 1 PARS score (x) or not.

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Chapter 11.5, Problem 11.77ACI

Chapter 11.5, Problem 11.79ACI

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To obtain : The correlation coefficient r and interpret the results.

Solution Summary: The author explains that the correlation coefficient r is 0.727. There is moderately strong positive linear relationship between the PARS scores in year 1 and year 2.