Question

provide the following: Sr, t statistic, critical t value, and the statistical decision regarding

H0: ρ= 0

r= .17, n= 62, α= .01, two-tailed test

Answer 1

Solution:

From given information , the hypothesis can be written as ,

H₀ : = 0 vs H₁ :     0

n = 62

r = 0.17

α= .01

The test statistic is given by

t =

=  

= 1.336

Test statistic t = 1.336

Now , df = n - 2 = 62 - 2 = 60

α= 0.01

α/2 = 0.005

Given that , Two tailed test

So , there are two critical values.

=   t_0.005,60 = 2.660

Critical values are -2.660 and 2.660

Rejection region : t < -2.660 or t > 2.660

Our test statistic t = 1.336

It does not fall in rejection region.

So ,

Do not reject the null hypothesis H₀

There is no evidence to conclude that there is significant correlation between two variables.