Question

Determine whether the given correlation coefficient is statistically significant at the specified level of significance and sample size.

r=0.418 , α=0.01, n=20

Answer 1

Solution:

Here, we have to use t test for the population correlation coefficient.

The null and alternative hypotheses for this test are given as below:

H₀: ρ = 0

H_a: ρ ≠ 0

This is a two tailed test.

We are given

Level of significance = α = 0.01

From given data, we have

Sample size = n = 20

df = n – 2 = 18

Critical value = -2.88 and 2.88

(by using t-table)

Sample correlation coefficient = r = 0.418

The test statistic formula is given as below:

t = r*sqrt(n – 2)/sqrt(1 – r^2)

t = 0.418*sqrt(20 - 2)/sqrt(1 - 0.418^2)

t = 1.95

Test statistic = 1.95

Critical value = -2.88 and 2.88

Test statistic is lies between Critical Values.

So, we do not reject the null hypothesis

There is not sufficient evidence to conclude that the given correlation coefficient is statistically significant.