Question

A random sample of 30 pair of observations from a normal population gives a correlation coefficient of 0.32 . Is it likely that the variable in the coefficient are correlated?

Answer 1

$H_0:r=0$ variables in the coefficient are not correlated

$H_a:r\neq0$ variables in the coefficient are correlated

$t=\frac{r\sqrt{n-2}}{1-r^2}=\frac{0.32\sqrt{30-2}}{1-0.32^2}=1.886$

$df=n-2=30-2=28$

for $\alpha=0.05$

critical value:

$t_{crit}=2.048$

Since $|t|<t_{crit}$ we accept null hypothesis. Variables in the coefficient are not correlated.