Question

What are the hypotheses for testing to see if a correlation is statistically significant?

• A.

  H₀: r = ±1; H₁: r≠ ± 1

• B.

  H₀: ρ = ±1 ; H₁:ρ≠ ±1

• C.

  H₀: ρ = 0; H₁:ρ=1

• D.

  H₀: r = 0; H₁: r≠ 0

• E.

  H₀: ρ = 0; H₁:ρ≠

Answer 1

The hypothesis to check that the correlation is statistically significant is:

E. H0: ρ = 0 ; H1:ρ ≠ 0

As here our null hypothesis is that the population correlation coefficient is 0 i.e. there is no significant relationship between the two variable and the alternative hypothesis is that the population correlation coefficient is ≠ 0 i.e. there is some relationship between the two variables and we carry out the test to identify if the relationship is significant to conclude that ρ ≠ 0 / correlation is statistically significant.