1. True or False, Justify for full credit-
(a) If the variance of a data set is zero, then all the observations in this data set are zero.
(b) If P(A) = 0.4 , P(B) = 0.5, and A and B are disjoint, then P(A AND B) = 0.9.
a. Assume X follows a continuous distribution which is symmetric about 0. If P(X > 2) = 0.3, then P(X < -3) ≤0.3.
b. A 95% confidence interval is wider than a 90% confidence interval of the same parameter.
c. In a right-tailed test, the value of the test statistic is 1.5. If we know the test statistic follows a Student's t-distribution with P(T < 1.5) = 0.96, then we fail to reject the null hypothesis at 0.05 level of significance.