Assignment 1 Due Date: February 3rd, 2015 – Corrections Due: February 17th, 2015 - Material Covered: Lessons 1-9. Question 1 GlobaTel, a large manufacturer of electrical parts used in cell phone, is about to launch a new product line. The company psychologist has been asked to administer a Depression, Anxiety, and Stress Test (DAST) to determine if employees are able to handle the transition to the new line, or if special training will be needed. A sample of 20 employees is randomly selected to complete the DAST test and their scores are listed below. The DAST scale ranges from 0 (no anxiety) to 25 (high anxiety). Employee DAST Score Employee DAST Score 1 2 3 4 5 6 7 8 9 10 0 4 7 1 19 9 12 8 1 5 11 12 13 14 15 16 17 18 19 20 23 12 9 4 0 0 3 2 6 2 a) Calculate the measures of central tendency for the results of the DAST: i. Mean ii. Median iii. Mode b) Calculate the measures of variability for the results of the DAST: i. Range ii. Standard Deviation c) Identify the measures of position of the DAST: i. P15 ii. P66 iii. the 5-number summary INTE 296 – Assignment 1 Question 2 Christy is an avid golf player. Each summer she tries to improve her game by changing golf clubs, trying new techniques, and getting tips from local pros. After each round that she plays at her favourite golf course, Christy records the scores into a database so that she can compile her annual statistics. Use the scores recorded in the graph below to help Christy calculate her statistics for this past season (Note: In golf, a lower score is better). Christy's Golf Scores 16 14 Frequency 12 10 8 6 4 2 0 80 81 82 83 84 85 86 87 88 89 90 91 92 Score a) Calculate the measures of central tendency for Christy’s golf scores for this past season: i. Mean ii. Median iii. Mode b) Calculate the measures of variability and position for Christy’s golf scores for this past season: i. Standard Deviation ii. IQR iii. P45 iv. P90 c) The reason that Christy records her scores is to determine if she is improving her golf game. What three suggestions can you give Christy to help her determine if her game is indeed improving? Your recommendations could also include suggestions about how to use the data she has collected, other variables she could collect in addition to her scores, and/or changes to the methodology of her study. INTE 296 – Assignment 1 Question 3 The Pinkerton Detective Agency, now called Pinkerton Government Services (PGS), was originally founded in 1850 when Allen Pinkerton, a coppersmith, helped arrest some counterfeiters in Dundee, U.S.A. Today, their 1800 agents offer more protective services than investigative services. The table below describes the agents in terms of their department and speciality, as well as their geographical area of work (U.S.A., Canada, or Puerto Rico). Department Protective Services Specialized Services Firefighters/EMT Services Speciality Security Console Operations Secure Satellite Launch Teams Technical Support Document/ Information Security Emergency Preparedness Services Train Firefighters and EMTs U.S.A. Number of Agents Canada Puerto Rico 140 50 45 50 40 15 470 245 115 230 45 65 45 130 35 30 20 30 Using this information, determine the theoretical probability that an agent chosen at random from among all Pinkerton employees… a) b) c) d) e) f) g) h) i) is a Security Console Operator is in the Specialized Services department works in Canada is a Document/Information Security Specialist and works in Puerto Rico works in the U.S.A. or is in the Firefighter/EMT Services department works in a Secure Satellite Launch Team given that they work in Canada they work in Puerto Rico given that they specialize in Emergency Preparedness Services they are not in the Protective Services department given that they work in the U.S.A. Is being a Technical Support Officer independent from working in Puerto Rico? Use the data from the table to justify your response (prove your theory using calculations). INTE 296 – Assignment 1 Question 4 The batteries to the remote control for your television have just run out. You find your collection of miscellaneous “AA” batteries and grab 2 of them to replace the used ones. The box you used to fish out the replacements contained 14 batteries, but you were unaware that 5 of them were faulty and did not work. a) If the remote control requires two good batteries to operate properly, what is the probability that the remote control now works properly? b) Given that the remote control is now working, what is the probability that the next two batteries you select from your remaining stash will also work? Question 5 Carol lives in the east end of Montreal. To get to school for her morning classes Carol has the option of taking the bus, going underground with the metro, or driving her car downtown to get to Concordia. Carol prefers the metro, especially in the winter, and she will opt for it 35% of the time. The bus is perhaps a more convenient option since it stops near her house, so she will choose that option 55% of the time. The car is the most expensive option, but it is the most reliable, as demonstrated by the fact that she is only late for class 5% of the time when she drives. The bus is the least reliable of the options as it gets Carol to class on time 65% of the time, whereas this value increases by 10% with the metro. a) b) c) d) e) What is the probability that Carol is late to class on a given morning? What is the probability that Carol took the metro and is on time for class? What is the probability that Carol drove to school and is on time for class? What is the probability that Carol opted for the bus given that she was late to class? What is the probability that Carol is on-time for class given that she did not drive? Question 6 You are tutoring a friend of yours who is enrolled in an introductory statistics class. They are struggling with the concept of conditional probability. Create and solve a problem to help demonstrate the concept to your friend where you differentiate between independent and dependent probabilities. Note: Your problem must be unique and cannot be plagiarised from the course material or from other sources. INTE 296 – Assignment 1

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