9.112 Bad P-value interpretations A random sample of size 1000 has x = 104. The significance level a is set at 0.05.

The P-value for testing H0: m = 100 against Ha: m • 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 m • 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 a = 0.05 level.

f. We can reject H0 at the a = 0.05 level.