True or False. Justify answers.

If the variance of a data set is zero, then all the observations in this data set are zero.

If P9A) = 0.4, P(B)=5 and A and B are disjoint, the P(A and B) = 0.9

Assume X follows a continuous distribution which is symmetric about 0. If P(X >2) = 0.3, then P (X<-3) less than or equal to 3.

A 95% confidence interval is wider than 90% confidence interval of the same parameter.

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 is at 0.05 level of significance.