Answer to Question #199159 in Statistics and Probability for mandona

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.