Examinations - 1 Murdoch Semester 2, 2020 UNIVERSITY MAS223 APPLIED STATISTICS Exam Type : CLOSED BOOK EXAM - THEORY Exam Duration : 3 hrs + 10 mins reading time (No note taking allowed) STUDENT DETAILS Surname: Given Name: Student No: Signature: INSTRUCTIONS Answer all questions in the space provided. If additional space is required, make use of the extra pages at the end of the exam. EXAMINATION AIDS ALLOWED Provided by the University NIL Provided by the Candidate 1 A4 SHEET (BOTH SIDES) HANDWRITTEN NOTES (NO PHOTO-REDUCTIONS) CALCULATOR LEVEL 2 - SCIENTIFIC EXAM PAPER MUST BE RETURNED TO EXAMS OFFICE AFTER EXAM
MAS223 Applied Statistics Final Exam - Second Semester, 2020 1. (11 marks) Background: Treatment times for an orthodontic procedure This data set will be used for questions one and two. A study on dental treatment time for orthodontic work was carried out with an enrolment period of two years. Patients were treated at either a public or private hospital. We have information on the patients including demographics, facial di- mensions pre treatment and surgical corrections, see Table 1 for a complete list of variables. We are interested in the impact of age at the start of treatment and hospital type on treatment time. Variable Description iD Unique identifier for the patient Treatment_time The total time of the treatment in days. Age Age (in years) at the start of the treatment Sex Sex of the patient Hospital Either private or public representing the type of hospital where the patients received their care. Note that private is just one particular private hospital and public is one particular public hospital. Skeletal AP Anteroposterior skeletal pattern pre-treatment. Skeletal V Vertical skeletal pattern pre-treatment. Skeletal T Transverse skeletal pattern pre-treatment. Surg _Max_AP Surgical correction - Anteroposterior maxillary. Surg Mand_AP Surgical correction - Anteroposterior mandibular. Table 1: Descriptions of variables collected on the treatment time for orthodontic work including treatment time, hospital, demographics, facial dimensions pre treatment and surgical corrections
MAS223 Applied Statistics Final Exam - Second Semester, 2020 Consider the treatment times for all patients. Table 2 provides descrip- tive statistics and Figure 1 shows graphical displays for these treatment times in days. Statistic Value Q1 (i.e., first quartile) X X (i.e., median) Q3 (i.e., third quartile) Range(X) MAD(X) SQ S IQR 522 685.6 657 67 1821 187 4775 273 245 Table 2: Descriptive statistics for treatment time in days Histogram and Density Plot of Dental Treatement Time 0.0020 ! 2000 0.0015 1 1500 Density 0.0010 1 Sample Quantiles 1000 0.0005 ! 500 P r T T 1 500 1000 1500 2000 0.0000 i Treatment time (day) Figure 1: Histogram with overlaid density plot times. Normal Q-Q Plot of Treatment time (day) -3 Theoratical Quantiles (left) and boxplot (right) of treatment /3
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