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ABS Business Statistics MATH 210 ABS Final test Academic year 2020-2021 Fall term Bruno Fischer Colonimos Time allowed: Documents : Calculator: Subject length: Poll 2h30mn Any Any personal pocket calculator 4 pages A polling firm has conducted an opinion poll among a group of citizens living in a certain area, regarding a tax reform being considered by the government. Respondents indicated their opinion on a scale of 1 (very unfavourable) to 5 (very favourable). They also answered other questions. Partial results are given in the following table: Id. Age 1 35 2 61 3 35 4 37 5 32 6 33 7 65 8 45 9 39 10 32 11 57 12 38 13 37 14 42 15 38 16 48 17 40 18 57 19 44 20 40 21 21 22 49 Gender Children Male Female Male Male Female Female Female Male Male Female Male Female Female Female Female Male Male Female Male Male Female Male HNONNDHNNNOHHWHNUUWNONH Salary Opinion 39200 37200 37900 31200 48800 27800 29800 27500 28600 35900 28900 34900 33600 32000 23400 36900 22600 22000 27100 35400 32600 37300 kaWhl'NNl'l'Wbthl'Ll'le'm Grading system (points): Presentation, legibility (bonus/malus) ...... i 5 point Poll ........................................................ 20 points Baker Enterprises .................................. 20 points Ward Doering Auto Sales ...................... 15 points Library ................................................... 15 points Service Station ....................................... 15 points Credit card Balances .............................. 15 points Total .................................................. 100 points Id. Age Gender Children Salary Opinion 23 34 Male 0 46800 3 24 49 Male 0 25900 5 25 40 Male 1 26700 3 26 38 Male 1 26000 1 27 27 Male 3 27200 2 28 63 Male 2 32300 1 29 52 Male 1 26500 3 30 51 Male 3 22300 3 Columns : ld.= respondent identification number, Age = age in years, Gender = selfexplanatory, Children = number of children, Salary 2 annual salary in euros. Opinion = opinion on a scale of 1 to 5 1. In this situation, what is the definition of a statistical individual? What is the population of this survey? What is the sample? What are the variables? What is their respective nature? (qualitative, quantitative discrete, quantitative continuous...) For the variable Gender, present a frequency distribution table and an appropriate graphical representation. For the variable Age, present a frequency distribution table. Explain clearly your choices (if any) Show an appropriate graph for this distribution Analyzing the variable Opinion, and considering separately the respondents who have 2 children or more, and those who have 0 or 1 child, one gets the following results: - Final Stats EN ABS 2020-21 VDD.docx- Bruno Fischer Colonimos, - page 1/4 - Children 0-1 child 2+ children Number of respondents 15 15 Mean 3.33 2.53 Standard deviation 1.25 1.36 Coefficient of variation 0.37 0.54 Minimum 1 1 First quartile Q1 3 1 Median 3 2 Third quartile 0.3 4 4 Maximum 5 5 What conclusions do these results suggest? Nota Bene : a. Your conclusions will be based on the results presented above. You may supplement these results with a boxplot (not mandatory). b. Be sure to comment on: The overall value of "Opinion\" 0 The variation of this opinion, from one respondent to another. Baker Enterprises The manager of Baker Enterprises must decide which of two numerically controlled milling machines to purchase. One criterion to be used for the decision is the monthly expected repair costs. The production manager, given the technical specifications of each machine, has assessed the following probability distribution, based on his experience: Machine B Repair cost (5) 500 0.2 500 0.2 1000 0.4 1000 0.3 5000 0.35 5000 0.4 10000 0.05 10000 0.1 Machine A Repair cost (S) Probability Probability Find the expected value and the standard deviation of the monthly repair cost, for each machine. What choice would this information suggest? Justify clearly. Ward Doering Auto Sales Ward Doering Auto Sales is considering offering a special service contract that will cover the cost of any service work required on leased vehicles. From experience, the company manager estimates that yearly service costs are approximately normally distributed, with a mean of $170 and a standard deviation of S25. If the company offers the service contract to customers for a yearly charge of $180, 1. What is the probability that any one customer's service costs will exceed the contract price of $180? 2. What is the probability that any one customer's service costs will be at least equal to $135 ? 3. What is the probability that any one customer's service costs will be between $135 and 5180? Library A library checks out an average of 320 books per day, with a standard deviation of 75 books. Consider a sample of 30 days of operation, with i? being the sample mean number of books checked out per day. 1. What is the sampling distribution of i? 2. What is the probability that the sample mean for 30 days will be between 310 and 330 books? 3. What is the probability that the sample mean for 30 days will be between higher than 340 books? Service Station A service station has recorded the number of gallons of gasoline sold to a sample of 30 cars. The data is listed in the table: 1. Compute the mean and the standard deviation of the sample. Give a point estimate for the population mean u and the population standard deviation 0. 2. Develop a 95% confidence interval for the mean number of gallons sold per car, for the population of cars being serviced at this station. Credit card balances A well-known bank credit card firm is interested in estimating the proportion of credit card holders that carry a nonzero balance at the end of the month and incur an interest charge. Assume that the desired precision (i.e. the maximum accepted margin of error) for the proportion estimate is i 0.05 (i.e. 5 percentage points) at a 95% confidence level. How large a sample would you recommend? Final Stats EN ABS 2020-21 V00.docx - Bruno Fischer Colonimos, - page 2/4 - Areas under the Standard Normal Curve The table gives cp(z) = p(0>n) Population size N (N>>n) Population mean : u Population proportion : p Population Standard deviation : 0 Sample Sample size: n (n 2 30) Sample size: n (n 2 30) Sample mean : a? Sample proportion : f Sample standard deviation 5 (special formula) Sampling distribution 32 ~ N01; 033), with of = % f ~ N0); of), with of = P(1n p) 2 Point Estimation Mean Proportion A mean: \"=3? Proportion: standard deviation (7' = 3 (special formula) 3 Interval estimation General format Parameter E [(oint estimate) i (critical value) x standard deviation 0 the estimator ] Mean Proportion 4 Critical values of the standard normal distribution Confidence level 90% 95% 99% - Final Stats EN ABS 2020-21 VDD.docx - Bruno Fischer Colonimos, - page 4/4