Question

if the correlation coefficient value for the two variables is 0.865 with sample size 15 each.what is the value of the test statistic, to test the significance of correlation

Answer 1

Answer:

if the correlation coefficient value for the two variables is 0.865 with sample size 15 each.what is the value of the test statistic, to test the significance of correlation

Answer 2

Given,

The correlation coefficient value(r)$\[ = 0.865\]$

The sample size(n)$\[ = 15\]$

To find,

The value of statistics to test the significance of correlation.

Solution,

Know that the formula for the value of statistics to test the significance of the correlation is $\[\frac{{r\sqrt {n - 2} }}{{\sqrt {1 - {r^2}} }}.\]$

Apply values.

Therefore,

$\[\begin{array}{l} \Rightarrow \frac{{0.865\sqrt {15 - 2} }}{{\sqrt {1 - {{\left( {0.865} \right)}^2}} }}\\ \Rightarrow \frac{{0.865 \times \sqrt {13} }}{{\sqrt {1 - 0.7482} }}\\ \Rightarrow \frac{{0.865 \times 3.6}}{{\sqrt {0.2517} }}\\ \Rightarrow 6.21\end{array}\]$

Hence, the value of statistics to test the significance of the correlation is$\[6.21\]$.