1. True or False. Justify for full credit. (25 pts)(a) If all the observations in a data set are identical, then the variance for this data set iszero.(b) If P(A) = 0.4 and P(B) = 0.5, then P(A AND B) = 0.2.(c) The mean is

1. True or False. Justify for full credit. (25 pts)(a) If all the observations in a data set are identical, then the variance for this data set iszero.(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 sameparameter.(e) In a two-tailed hypothesis testing at significance level α of 0.05, the test statistic iscalculated as 2. If P(X >2) = 0.03, then we have sufficient evidence to reject the nullhypothesis.