Prove that there is no homomorphism from Z16 ⊕ Z2 onto Z4 ⊕ Z4.
NORTHCENTRAL UNIVERSITY ASSIGNMENT COVER SHEET Student: THIS FORM MUST BE COMPLETELY FILLED IN Follow these procedures: If requested by your instructor, please include an assignment cover sheet. This will become the first page of your assignment. In addition, your assignment header should include your last name, first initial, course code, dash, and assignment number. This should be left justified, with the page number right justified. For example: Save a copy of your assignments: You may need to resubmit an assignment at your instructor’s request. Make sure you save your files in accessible location. Academic integrity: All work submitted in each course must be your own original work. This includes all assignments, exams, term papers, and other projects required by your instructor. Knowingly submitting another person’s work as your own, without properly citing the source of the work, is considered plagiarism. This will result in an unsatisfactory grade for the work submitted or for the entire course. It may also result in academic dismissal from the University. BTM701486 Garrett Fox, PhD Statistics Assignment 6 Faculty Use Only 2 Introduction The purpose of this week’s paper is to first locate an article in one of the major online magazines which includes not only a margin of error but a confidence interval. After locating the article, we are to evaluate and interpret the results to be able to provide an understanding of real world statistics application. The article of choice hosts a discussion of cocaine versus marijuana use within the United States. Schlanger (2014) has taken a crack at providing statistical data based upon the report issued by Rand corporation for the Whitehouse. Schlanger’s article sums up the report by showing that in the period from 2000 to 2010 that Americans cut their Cocaine use in half while doubling their marijuana use. In 2000, Cocaine use on average was double that of marijuana with an estimated sample size of 18 million Americans that smoke marijuana four or more times a day. The mean cocaine use is estimated at approximately $28 billion with range of $18 to $44 billion. The report itself discussed the 95% confidence interval based upon the arrests of adult males where a positive drug test was found. The reports are filled with levels of uncertainty due to not having a solid sample population of overall users in America. Since they can only base the statistics on a given population that is adult, male, and arrested, the statistics are certainly skewed. The margin for error is extraordinarily high. The Rand organization takes the data from a very small population within each drug category and is attempting to provide an estimation of numbers and drug use type built upon what appears to be a flawed strategy. The report itself discusses the estimates are just that, estimates and the margin for error, significant (Rand Corporation, 2014). While the information provided by the Rand Corporation could help provide estimates of drug 3 use in the U.S., but the margin of error is high due to the lack of an appropriate sample population. Conclusion The purpose of this week’s paper was to first locate an article in one of the major online magazines which includes not only a margin of error but a confidence interval. After locating the article, I evaluated and interpreted the results to be able to provide an understanding of real world statistics application. In the case of drug use within the U.S., one can see that the information is provided on a sample population that certainly does not include the overall American population. As an effective researcher, one must have an understanding the sample population and how to read the data rather than taking the information at face value. 4 References Rand Corporation. (2014). What America’s Users Spend on Illegal Drugs: 20002010. Retrieved from https://www.whitehouse.gov/sites/default/files/ondcp/policyand research/wausid_results_report.pdf Schlanger Z. (2014). Cocaine usage way down but marijuana picks up the slack. Retrieved from http://www.newsweek.com/authors/zoeschlanger