STAT 200 FINAL EXAM A

Answer all 25 questions. Make sure your answers are as complete as possible. Show all of your work and reasoning. In particular, when there are calculations involved, you must show how you come up with your answers with critical work and/or necessary tables. Answers that come straight from programs or software packages will not be accepted. If you need to use software (for example, Excel) and /or online or hand-held calculators to aid in your calculation, please cite the sources and explain how you get the results. 1. 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. No, all the observations will be same but it is not necessary that all the observations will be zero, because if all the observations are same even then the variance will be zero. (b) If P(A) = 0.4 , P(B) = 0.5, and A and B are disjoint, then P(A AND B) = 0.9. No, because if A and B are disjoint then P(A AND B) = 0. (c) Assume X follows a continuous distribution which is symmetric about 0. If , then . Yes, P(X-3) will be less than 0.3 because the value will be towards negative side. (d) A 95% confidence interval is wider than a 90% confidence interval of the same parameter. Yes, a 95% confidence interval is wider than a 90% confidence interval of the same parameter because increasing the confidence limit we increases the acceptance region and reduces the rejection region. (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 . No, we will not be able to reject the null hypoth