I roll a die 600 times, and it comes up 130 times with face 6.

My hypotheses are H0 : the die is fair, and H1 : the die is not fair. The P-value is 0.002. Say whether each of the following statements is true or false, and briefly explain each of your answers.

a. TheP-value is 2P(X ≥ 130) where X ∼ Binomial(600, 1/6).

b. TheP-value is 2P(X ≤ 130) where X ∼ Binomial(600, 1/6).

c. The P-value of 0.002 specifies that this result is very unusual with a fair die, so we suspect we might not have a fair die.

d. The P-value of 0.002 means that there is only a 0.2%

chance that the die is fair.

e. A fair die would give a P-value ≤ 0.002 in about 0.2% of similar experiments.