A random sample of size 50 has ¯y = 130. The P-value for testing H0: μ = 120 against Ha: μ = 120 is P = 0.069.

Explain what is incorrect about each of the following interpretations of this P-value, and provide a proper interpretation.

(a) The probability that the null hypothesis is correct equals 0.069.

(b) The probability that ¯y = 130 if H0 is true equals 0.069.

(c) If in fact μ = 120, the probability that the data would at least be as contradictory to H0 as the observed data equals 0.069.

(d) The probability of Type I error equals 0.069.

(e) We can accept H0 at the α = 0.06 level.

(f) We can reject H0 at the α = 0.06 level.