Question

Suppose the correlation coefficient is 0.80 and the number of observations is 62. What is the calculated test statistic? Is this significant correlation using a 1% level of significance? 2. Given that, r = 0.475 N = 10, Is this significant correlation between X and Y using a 5% level of significance? 

Answer 1

$H0:\rho=0$

$Ha:\rho\ne0$

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

$t=\frac{0.8\sqrt{60}}{\sqrt{1-0.8^2}}=10.33$

$Cv=t_{60,0.005}=-2.66, 2.66,$

10.33 falls in the rejection region. 10.33>2.66, this, we reject H0 and conclude that the correlation is significant.

2.

$H0:\rho=0$

$Ha:\rho\ne0$

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

$t=\frac{0.475\sqrt{8}}{\sqrt{1-0.475^2}}=1.53$

$Cv=t_{8,0.025}=-2.306, 2.306.$

1.5<2.306, we fail to reject the null hypothesis and conclude that there is no significant correlation between X and Y.