A one-sample z-test for a proportion at the 0.01 significance level of will be conducted for the following set of hypotheses. For which of the following is the probability of a type error the greatest?
a) Null hypothesis: p = 0.5, Alternative hypothesis: p ≠ 0.5
b) Null hypothesis: p = 0.3, Alternative hypothesis: p > 0.3
c) Null hypothesis: p = 0.7, Alternative hypothesis: p < 0.7
d) Null hypothesis: p = 0.9, Alternative hypothesis: p ≠ 0.9