True or False. Justify for full credit.

(a) If P(A) = 0.4 , P(B) = 0.5, and A and B are disjoint, then P(A AND B) = 0.2.

(b) If all the observations in a data set are identical, then the variance for this data set is 0.

(c) The mean is always equal to the median for a normal distribution.

(d) Its easier to reject the null hypothesis at significance level of 0.01 than at significance level of 0.05. (e) In a two-tailed test, the value of the test statistic is 2. If we know the test statistic follows a Students t-distribution with P(T >2) = 0.03, then we have sufficient evidence to reject the null hypothesis at 0.05 level of significance.