Given the linear correlation coefficient r and the sample si

Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05. (5 pts.) r = -0.778, n = 7

Solution

Set Up Hypothesis
Under The Null Hypothesis H0: =0
Under The Alternate Hypothesis H1: !=0
Test Statistic
Value of ( r ) =-0.778
Number (n)=7
we use Test Statistic (t) = r / Sqrt(1-r^2/(n-2))
to=-0.778/(Sqrt( ( 1--0.778^2 )/(7-2) )
to =-2.77
|to | =2.77
Critical Value
The Value of |t | at LOS 0.05% is 2.571
We got |to| =2.77 & | t | =2.571
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho