Given this result from a nondirectional Pearsons correlation

Given this result from a non-directional Pearson’s correlation: r (13) = .78, p <.01

a What was the sample size?

b What was alpha?

c What was the critical value?

d Is the relationship positive or negative?

e What was the value for t?

f Did the researcher conclude the relationship was statistically significant?

Solution

r (13) = .78, p <.01

Set Up Hypothesis
Null, H0: =0
Alternate, H1: !=0
Test Statistic
Value of ( r ) =-0.78
Number (n)=13
we use Test Statistic (t) = r / Sqrt(1-r^2/(n-2))
to=-0.78/(Sqrt( ( 1--0.78^2 )/(13-2) )
to =-4.13
|to | =4.13
Critical Value
The Value of |t | at LOS 0.01% is 3.106
We got |to| =4.13 & | t | =3.106
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho

a. What was the sample size?
sample size(n) = 13

b. What was alpha?
Alpha, 0.01

c. What was the critical value?
| t | = 3.106

d.Is the relationship positive or negative?
Negative

e. What was the value for t?
to =-4.13

f. Did the researcher conclude the relationship was statistically significant?
Yes,the relationship was statistically significant