Suppose in a two-tailed test of H 0 : = 0 vs H a :

Suppose in a two-tailed test of H₀: ρ = 0 vs H_a: ρ ≠ 0, we reject H0 when using a 5% significance level. Which of the conclusions below (if any) would also definitely be valid for the same data? Explain your reasoning in each case.

(a) Reject H₀: ρ = 0 in favor of H_a: ρ ≠ 0 at a 1% significance level.

(b) Reject H₀: ρ = 0 in favor of H_a: ρ ≠ 0 at a 10% significance level.

(c) Reject H₀: ρ = 0 in favor of the one-tail alternative, H_a : ρ > 0, at a 5% significance level, assuming the sample correlation is positive.