True or False. Justify for full credit.

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

(b) If P(A) = 0.4 and P(B) = 0.5, then P(A AND B) = 0.2.

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

(d) A 95% confidence interval is wider than a 90% confidence interval of the same parameter.

(e) In a two-tailed hypothesis testing at significance level α of 0.05, the test statistic is calculated as