A random sample of size 40 has ¯y = 120. The Pvalue for testing H0: μ = 100 against Ha: μ = 100 is P = 0.057.

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 0.057.

(b) The probability that ¯y = 120 if H0 is true equals 0.057.

(c) If in fact μ = 100, the probability equals 0.057 that the data would be at least as contradictory to H0 as the observed data.

(d) The probability of Type I error equals 0.057.

(e) We can accept H0 at the α = 0.05 level.

(f) We can reject H0 at the α = 0.05 level.