True or False. Justify for full credit. (a)If the variance of a data set is zero

Question

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.

Explanation / Answer

(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.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.