Question

Find out ‘r’.: n=16;P.E = 0.125​

Answer 1

Step-by-step explanation:

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Answer 2

The value of 'r' is  $\sqrt{0.25816}$

Step-by-step explanation:

Given:

N = 16

PE = 0.125​

To find: Value of 'r'  which is the correlation coefficient of ‘N’ pairs of observations

Formula used:

Probable Error$=0.674 \times \frac{1-r^{2}}{\sqrt{N}}$

• Where N is the number of observations
• PE is the probable error
• r is the correlation coefficient of ‘N’ pairs of observations

Solution:

We have

N = 16

PE = 0.125​

Substitute in the equation

$0.125 =0.674 \times \frac{1-r^{2}}{\sqrt{16}}$

$\frac{0.674\left(1-r^{2}\right)}{4}=0.125$

Multiply both sides by 4

$\frac{0.674\left(1-r^{2}\right)}{4} \times 4=0.125 \times 4$

Simplify

$0.674\left(1-r^{2}\right)=0.5$

$0.674-0.674 r^{2}=0.5$

Subtract 0.674 from both sides

$0.674-0.674 r^{2}-0.674=0.5-0.674$

Simplify

$-0.674 r^{2}=-0.174$

Divide both sides by -0.674

$\frac{-0.674 r^{2}}{-0.674}=\frac{-0.174}{-0.674}$

Simplify

$r^{2}=0.25816$

$r=\sqrt{0.25816}$

Then the correlation coefficient of ‘N’ pairs of observations $r=\sqrt{0.25816}$