True or False Justify for full credit a If 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 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 .

Solution

a)

False. If the variance is 0, the all observations are equal.

b)

FALSE. P(A and B) = 0 for disjoint events.

c)

TRUE. P(x<=-2) = 0.3. As P(x<=-3) is just a subset of P(x<=-2), then P(x<=-3) <= 0.3. [answer]

d)

TRUE. This is because the critical z or t values are larger for larger confidence levels.

e)

False. The right tailed area of t = 1.5 here is 1 - 0.96 = 0.04. Thus, the P value = 0.04.

As P < 0.05, we reject the null hypothesis.