Consider the hypothesis test X ∼ Binomial(n, p)

H0 : p = 0.5 H1 : p , 0.5.

We observe X = x. Say whether each of the following statements is true or false. If the statement is false, explain why.

a. If we fix the sample size n, the P-value becomes smaller as x gets further away from 0.5n.

b. A small P-value means that the sample size n must be large.

c. A small P-value means that x must be a long way from 0.5n.

d. The P-value alone tells us nothing about how far away x is from 0.5n