True or False. Justify for full credit.

(a) A is an event, and Ac is the complement of A, then P(A OR Ac ) = 0.

(b) If the variance of a data set is 0, then all the observations in this data set must be identical.

(c) If a 95% confidence interval for a population mean contains 1, then the 99% confidence interval for the same parameter must contain 1

(d) When plotted on the same graph, a distribution with a mean of 60 and a standard deviation of 5 will look more spread out than a distribution with a mean of 40 and standard deviation of 8.

(e) In a right-tailed test, the value of the test statistic is 2. The test statistic follows a distribution with the distribution curve shown below. If we know the shaded area is 0.03, then we have sufficient evidence to reject the null hypothesis at 0.05 level of significance.