STAT 200 final, student's complete answer sheet. 2022 update

STAT 200 Final Examination Fall 2016 OL4/US2 Page 1 of 15 STAT 200 Introduction to Statistics Name ______________________________ Final Examination: Fall 2016 OL4/US2 Instructor _________________________ Answer Sheet Instructions: This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator. Record your answers and work in this document. Answer all 20 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 calculators, programs or software packages without explanation will not be accepted. If you need to use technology to aid in your calculation, you have to cite the source and explain how you get the results. For example, state the Excel function along with the required parameters when using Excel; describe the detailed steps when using a hand-held calculator; or provide the URL and detailed steps when using an online calculator, and so on. Show all supporting work and write all answers in the spaces allotted on the following pages. You may type your work using plain-text formatting or an equation editor, or you may handwrite your work and scan it. In either case, show work neatly and correctly, following standard mathematical conventions. Each step should follow clearly and completely from the previous step. If necessary, you may attach extra pages. You must complete the exam individually. Neither collaboration nor consultation with others is allowed. It is a violation of the UMUC Academic Dishonesty and Plagiarism policy to use unauthorized materials or work from others. Your exam will receive a zero grade unless you complete the following honor statement. Please sign (or type) your name below the following honor statement: I understand that it is a violation of the UMUC Academic Dishonesty and Plagiarism policy to use unauthorized materials or work from others. I promise that I did not discuss any aspect of this exam with anyone other than my instructor. I further promise that I neither gave nor received any unauthorized assistance on this exam, and that the work presented herein is entirely my own. Name _____________________ Date__________________ STAT 200 Final Examination Fall 2016 OL4/US2 Page 2 of 15 Record your answers and work. Proble m Number Solution 1 Answer: (a) True (b) False (c) False (d) False (e) True Justification: (a) A is an event, and Ac is the complement of A, then P(A AND Ac ) = 0. justification A and Ac ( complement of A) share no common region , and thus P(A AND Ac ) = 0. Therefore the statement is true (b). If the variance of a data set is 0, then all the observations in this data set must be zero. Justification Variance is usually the expectation or mean of the squared deviation of a random variable from its mean. If the variance is zero, the squared deviations must be zero and thus the mean must be equal to every value. So , a variance of zero implies the observations are identical (c). If a 95% confidence interval for a population mean contains 1, then the 90% confidence interval for the same parameter must contain 1 Justification Confidence interval z-values: 90% confidence interval Z= 1.645 , For 95% confidence interval , Z= 1,96 To compute the confidence interval , we multiply the z -values with the standard error. Since 90% Confidence interval is smaller than that of 95% confidence interval, the condition will not always be met . Therefore, the statement is false. d) When plotted on the same graph, a distribution with a mean of 40 and a standard deviation of 10 will look more spread out than a distribution with a mean of 50 and standard deviation of 5. Justification The spread of the distribution is directly related to size