Question

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A magazine tested paints. The table below shows the overall quality score and cost in dollars per gallon. Use the rank correlation coefficient to test for a correlation between the two variables. Use a significance level of a = 0.01. Based on these results, do you get better quality paint by paying more? 73 Quality Cost 78 19 84 18 66 27 74 15 84 18 77 30 63 24 75 19 20 69 21 68 O 15 What are the null and alternative hypotheses? O A. Ho: Ps+0 B. Ho: Ps #rs H: Ps=rs Hj: Ps = 0 C. Ho: Ps = rs H₂: Pstrs D. Ho: Ps = 0 Hj: Ps #0 Calculate the test statistic. Is (Round to three decimal places as needed.)

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Answer 1

Question 1

$r = ( ( N * \Sigma XY) - \Sigma X \Sigma Y) / (\sqrt{ (N \Sigma (X^{2}) - (\Sigma X)^{2} )(N \Sigma (Y^{2}) - (\Sigma Y)^{2} })$
$r = ( ( 11 * 16574 ) - 811 * 226 ) / ( \sqrt{ ( 11 * 60265 ) - ( 811 )^{2} )( 11 * 4866 ) - ( 226 )^{2} })$
r = -0.272

Test Statistic :-
t = (r * √(n - 2) / (√(1 - r2))
t = ( -0.2725 * √(11 - 2) ) / (√(1 - 0.0743) )
t = - 0.850

Question 2

$r = ( ( N * \Sigma XY) - \Sigma X \Sigma Y) / (\sqrt{ (N \Sigma (X^{2}) - (\Sigma X)^{2} )(N \Sigma (Y^{2}) - (\Sigma Y)^{2} })$

r = 0.405

7= (8*659046.2)-8043*653)/(V(8 * 8237741) -(8043)2)(8 * 53560.44) – (653)2)

Test Statistic :-
t = (r * √(n - 2) / (√(1 - r2))
t = ( 0.4046 * √(8 - 2) ) / (√(1 - 0.1637) )
t = 1.084

Question 3

$r = ( ( N * \Sigma XY) - \Sigma X \Sigma Y) / (\sqrt{ (N \Sigma (X^{2}) - (\Sigma X)^{2} )(N \Sigma (Y^{2}) - (\Sigma Y)^{2} })$
$r = ( ( 9 * 2227 ) - 178 * 107 ) / ( \sqrt{ ( 9 * 3674 ) - ( 178 )^{2} )( 9 * 1433 ) - ( 107 )^{2} })$
r = 0.705

Test Statistic :-
t = (r * √(n - 2) / (√(1 - r2))
t = ( 0.7048 * √(9 - 2) ) / (√(1 - 0.4967) )
t = 2.628