A researcher measures the relationship between sleep medication use (times used

Question

A researcher measures the relationship between sleep medication use (times used per week) and time spent working (in hours per week). Answer the following questions based on the results provided. Sleep Medication Use Time Spent Working 10 16 5 38 8 17 4 32 Part (a) Compute the Pearson correlation coefficient. (Round your answer to three decimal places.) Part (b) Multiply each measurement of drug use times 3 and recalculate the correlation coefficient. (Round your answer to three decimal places.) Part (c) Divide each measurement in half for time spent working and recalculate the correlation coefficient. (Round your answer to three decimal places.) Part (d) True or false: Multiplying or dividing a positive constant to one set of scores (X or Y) does not change the correlation coefficient. Note: Use your answers in (a) to (c) to answer true or false. True False

Explanation / Answer

Ans:

a)

r=sxy/sxx*syy

r=(4*701-30*103)/(SQRT(4*242-30^2)*SQRT(4*3013-103^2))=-0.913

b)

=(4*2103-90*103)/(SQRT(4*2178-90^2)*SQRT(4*3013-103^2))=-0.913

c)

r=(4*350.5-30*51.5)/(SQRT(4*242-30^2)*SQRT(4*753.25-51.5^2))=-0.913

d)In above three cases,correlation cofficient is same.

Multiplying or dividing a positive constant to one set of scores (X or Y) does not change the correlation coefficient. (True)

Sleep Medication Use(x) Time Spent Working(y) xy x^2 y^2 10 16 160 100 256 6 38 228 36 1444 9 17 153 81 289 5 32 160 25 1024 Total 30 103 701 242 3013

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