Question

Consider the following competing hypotheses:

H₀: ρ_xy = 0
H_A: ρ_xy ≠ 0

The sample consists of 16 observations and the sample correlation coefficient is 0.27. [You may find it useful to reference the t table.]

a-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

Answer 1

Given ,

Sample correlation coefficient = r = 0.27

Sample size = n = 16

Hypothesis :

Two tailed test.

Test statistic -

Critical value :

Let, significance level = = 0.05

Degrees of freedom = df = n - 2 = 16 - 2 = 14

Using Excel, =TINV( , df ) , This function returns two tailed inverse of t distribution

=TINV( 0.05 , 14 ) = 2.145

So, t critical value's for this two tailed test is ,

   and

                     

Decision about null hypothesis :

Rule : Reject null hypothesis if test statistic t < - 2.145 or t > 2.145

It is observed that test statistic t = 1.049 is less than 2.145 and greater than -2.145.

So, Do not reject null hypothesis.

Conclusion :

There is not sufficient evidence to conclude that variables are correlated.