True or False Justify for full credit aIf the variance of a

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 Aand B are disjoint, then P(A AND B) = 0.9.

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

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

(e)In a right-tailed test, the value of the test statistic is 1.5. If we knowthe test statistic follows a Student’s t-distribution withP(T< 1.5) = 0.96, then we fail to reject the null hypothesis at 0.05level of significance.

Solution

(a) False. Since if the variance of data set is zero, the all the observations in this data set are equal (not zero).

(b) False. If A and B are disjoint or mutually exclustive then P(A and B) = 0. (but not 0.9)

(c) False. If X is continout distribution which is symeetric about 0 and P(X>2) = 03 then P(X<-2) =0.3

(d) False: The 90% confidence interval is wider than 95% confidence interval of the same parameter.

(e) False: Given P(T<1.5) = 0.96 therfore, P-Value = 0.04 which is less than alpha (0.05) , we reject H0.