1. A researcher measures the relationship between Internet use (hours per week)

Question

1. A researcher measures the relationship between Internet use (hours per week) and social interaction (hours per week) in a sample of 10 students. The following table lists the hypothetical results of this study.

(a) Compute the Pearson correlation coefficient. (Round your answer to three decimal places.)


(b) Compute the coefficient of determination. (Round your answer to three decimal places.)

2. Employers often use standardized measures to gauge how likely it is that a new employee with little to no experience will succeed in their company. One such factor is intelligence, measured using the Intelligence Quotient (IQ). To show that this factor is related to job success, an organizational psychologist measures the IQ score and job performance (in units sold per day) in a sample of 10 new employees.

(a) Convert the following data to ranks and then compute a Spearman correlation coefficient. (Round your answer to three decimal places.)

Internet Use Social Interaction X Y 7 4 7 7 4 7 8 5 11 6 3 8 2 3 7 6 3 10 12 2

Explanation / Answer

Solution:-

1.a)

X Values
= 64
Mean = 6.4
(X - Mx)2 = SSx = 104.4

Y Values
= 58
Mean = 5.8
(Y - My)2 = SSy = 51.6

X and Y Combined
N = 10
(X - Mx)(Y - My) = -34.2

R Calculation
r = ((X - My)(Y - Mx)) / ((SSx)(SSy))

r = -34.2 / ((104.4)(51.6)) = -0.466

Meta Numerics (cross-check)
r = -0.466

1.b) r2  = (-.466)2= 0.217

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