Question

The data below are the final exam scores of 10 randomly selected statistics students and the number of hours they studied for the exam. Calculate the correlation coefficient.Hours (x) 8 10 7 13 7 9 9 10 11 8Scores (y) 60 75 55 83 61 73 80 85 85 66(A) 0.991(B) 0.761(C) 0.654(D) 0.847

Answer 1

Answer:

$r=\frac{10(6811)-(92)(723)}{\sqrt{[10(878) -(92)^2][10(53395) -(723)^2]}}=0.8465$  

So then the correlation coefficient would be r =0.8465

And the best options would be:

(D) 0.847

Step-by-step explanation:

Previous concepts

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

And in order to calculate the correlation coefficient we can use this formula:  

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

Solution to the problem

Data given:

 X: 8 10 7 13 7 9 9 10 11 8

Y: 60 75 55 83 61 73 80 85 85 66

For our case we have this:

n=10 $\sum x = 92, \sum y = 723, \sum xy = 6811, \sum x^2 =878, \sum y^2 =53395$  

And if we replace into the formula we got:

$r=\frac{10(6811)-(92)(723)}{\sqrt{[10(878) -(92)^2][10(53395) -(723)^2]}}=0.8465$  

So then the correlation coefficient would be r =0.8465

And the best options would be:

(D) 0.847

Answer 2

The correlation coefficient is (D) 0.847

Correlation coefficients are used to measure how strong a relationship is between two variables.  It's denoted by r and its always between -1 and 1.

We know the correlation coefficient formula is:  

$r=\frac{\sum xy-\sum x.\sum y}{n\sum x^{2} -\sum(x)^{2}-n\sum y^{2} -\sum(y)^{2}}$  

We have given data:

Hours X:    8    10   7   13   7    9    9   10   11   8

Scores Y:   60   75  55  83  61  73  80  85  85   66

In this case we have:

n=10  

And $\sum x=92,\sum y=723,\sum xy=6811,\sum x^{2} =878, \sum y^{2} =53395$

Substituting the values in the co relation formula, we get

$r=\frac{10(6811)-92(723)}{[10(878)-92^{2}][10(5335)-723^{2} } \\r=0.847$

 Therefore, the correlation coefficient is r =0.8465

So, the correct option is (D).

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