State whether each of the following is true or false.
a. The significance level of a test is the probability that the null hypothesis is false.
b. A Type I error occurs when a true null hypothesis is rejected.
c. A null hypothesis is rejected at the 0.025 level but is not rejected at the 0.01 level. This means that the p-value of the test is between 0.01 and 0.025.
d. The power of a test is the probability of accepting a null hypothesis that is true.
e. If a null hypothesis is rejected against an alternative at the 5% level, then using the same data, it must be rejected against that alternative at the 1% level.
f. If a null hypothesis is rejected against an alternative at the 1% level, then using the same data, it must be rejected against the alternative at the 5% level.
g. The p-value of a test is the probability that the null hypothesis is true.