Suppose that data are obtained from 20 pairs of (x, y) and the sample correlation coefficient is 0.75.

(a) Test the hypothesis that H₀: ρ = 0 against H₁: ρ> 0 with α = 0.05. Calculate the P-value.

(b) Test the hypothesis that H₁: ρ = 0.5 against H₁: ρ> 0.5 with α = 0.05. Calculate the P-value.

(c) Construct a 95% one-sided confidence interval for the correlation coefficient. Explain how the questions in parts (a) and (b) could be answered with a confidence interval.