Chapter 9, Problem 112CP

Bad P-value interpretations A random sample of size 1000 has $\bar{x}=104$. The significance level a is set at 0.05. The P-value for testing H₀: μ = 100 against H_a: μ ≠ 100 is 0.057. Explain what is incorrect about each of the following interpretations of this P-value and provide a proper interpretation.

1. a. The probability that the null hypothesis is correct equals 0.057.
2. b. The probability that $\bar{x}=104$ if H₀ is true equals 0.057.
3. 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.
4. d. The probability of a Type I error equals 0.057.
5. e. We can accept H₀ at the α = 0.05 level.
6. f. We can reject H₀ at the α = 0.05 level.