A random sample of size 1000 has x = 104. The significance level α is set at 0.05. The P-value for testing H0: μ = 100 against Ha: μ ≠ 100 is 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 x = 104 if H0 is true equals 0.057.
c. If in fact μ ≠ 100 so H0 is false, the probability equals 0.057 that the data would show at least as much evidence against H0 as the observed data.
d. The probability of a 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.