Answer true or false for each of the following, and explain your answer:

(a) P (Type II error) always increases with P (Type I error).

(b) If we accept HA using α = 0.01, then we also accept it using α = 0.05.

(c) The P-value is the probability that HA is false. (Hint:

Do we find probabilities about variables and their statistics, or about parameters?)

(d) Asurvey conducted by anNGOreports P = 0.082 for testing H0: μ = 0 against Ha: μ = 0. If the surveyors had instead reported a 99% confidence interval for μ, then the interval would have contained 0, and readers could have better judged just which values are plausible for μ.