1. True or False. Justify for full credit. (15 pts)

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

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(b) If P(A) = 0.4 , P(B) = 0.5, and A and 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 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 .




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