1. Are the following statements about p-values correct or not? Give reasons.

(a) A p-value is the probability that the null hypothesis is true.

(b) A p-value is the probability of observing the test statistic, or a more extreme statistic, under the assumption that the null hypothesis is true

(c) We should always use 0.05 as the significance level

(d) A small p-value proves the null hypothesis isn't true

(e) A p-value of 0.0001 is strong evidence against the null hypothesis

(f) If we fail to reject the null hypothesis (p-value is large) the null hypothesis is true