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

H0 : p = 0.5 H1 : p , 0.5.

The sample proportion is x/n. Say whether each of the following statements is true or false. If the statement is false, say why.

a. If the sample size n is fixed, the P-value becomes smaller as the sample proportion x/n moves further away from 0.5.

b. We’ll always get a smaller P-value if x/n = 0.3 than we will if x/n = 0.4, even if n differs between the two cases.

c. We’ll get a smaller P-value if x/n = 0.3 than if x/n = 0.4, if n is the same in both cases.

d. A P-value of 0.02 means there is quite a large difference between x/n and 0.5.