Does the value of the sample linear correlation coefficient

Does the value of the sample linear correlation coefficient, r, indicate that there is a linear

dependency between the two variables in the population from which the sample was drawn?

Briefly explain how to answer this question

Solution

For this we need to perform hypothesis test.

Let be the linear correlation coefficient of the population.

Hypotheses:

H0: = 0 (the two variables are not correlated at the level of the entire p

Ha: 6= 0, < 0 or > 0 (two-tailed, lower-tailed or upper-tailed test)

Determination of the test criteria:

significance level:

Find critical region, r

calculate the value of test statistics, r*

Decision:

Compare r* and r

if r* > r then reject H0; else, accept H0.