Assessment details for all students Assessment item 2???Assignment 2 ASSESSMENT Due date: 6:00pm, Friday Week 10 Weighting: 20% Format: Submit one file online as .doc, .docx, .rtf or .pdf 2 Assessment criteria This assignment must be typed, word-processed or clearly hand-written (since the assignment must be submitted electronically as a single file) and an appropriate equation editor should be used. Important note: There is no need to include the text of the assignment questions in your submission. Microsoft Excel allows students to cut and paste information easily into Microsoft Word documents. Word also allows the use of Microsoft Equation Editor to produce all necessary formulae (use of these are recommended). It is expected that Excel would be used to assist in statistical calculations for questions in this assignment. Where Excel is used, use copy function, \"Snipping tool\" or similar to cut and paste relevant parts of the spreadsheet to verify that you have done the work. For those questions where Excel is not used, all formulae and working must be included to obtain full marks. Only one file will be accepted in any of the formats mentioned above. No zipped file or any other file extension will be accepted. There will be late submission penalty for submissions beyond the deadline unless prior approval is obtained from the Course Coordinator through the extension system in Moodle. Under no circumstances any submission that is late beyond 14 days from the deadline will be marked, or get any score other than zero. Assignment markers will be looking for answers which demonstrate the student's ability to interpret and apply the statistical techniques in the scenarios and use statistical techniques as decision making tools in the business environment. Full marks will not be awarded to answers which simply demonstrate statistical procedures without comment, interpretation or discussion (as directed in the questions). Plagiarism CQU values academic honesty. Consequently, plagiarism will not be tolerated in assessment items. This assignment must be completed by each student individually. 1 of 10 Question 1 4 Marks Visit the Australian Stock Exchange website, www.asx.com.au and from \"Prices and research\" dropdown menu, select \"Company information\". Type in the ASX code \"CCL\" (Coca-Cola Amatil Limited), and find out details about the company. Your task will be to get the opening prices of a CCL share for every quarter from January 2001 to December 2015. If you are working with the monthly prices, read the values in the beginning of every Quarter (January, April, July, October) for every year from 2001 to 2015. It is part of the assignment task to test your ability to find the information from an appropriate website. If you are unable to do so, you may read the values from the chart provided below obtained from Etrade Australia. Obviously, reading from the chart will not be accurate and you may expect around 60 percent marks with such inaccuracy. After you have recorded the share prices, answer the following questions: (a) List all the values in a table and then construct a stem-and-leaf display for the data. 1 mark (b) Construct a relative frequency histogram for these data with equal class widths, the first class being \"$4 to less than $6\". 1 mark (c) Briefly describe what the histogram and the stem-and-leaf display tell you about the data. What effects would there be if the class width is doubled, which means the first class will be \"$4 to less than $8\"? 1 mark (d) What proportion of stock prices were above $10? (Note: Use only the original values of share prices and not adjusted values.) 2 of 10 1 mark Question 2 4 Marks The following table provides the median weekly rents of a 3-bedroom house of a few randomly selected suburbs in four capital cities of Australia - Sydney, Melbourne, Brisbane and Perth - for March 2016. The data is obtained from the website https://www.realestate.com.au/neighbourhoods/. From the data answer the questions below for the capital cities. (a) Compute the mean, median, first quartile, and third quartile for each capital city (with only the data provided for that city, do not add/delete values for any new/given suburb of question 2) using the exact position, (n+1)f, where n is the number of observations and f the relevant fraction for the quartile. 1 mark (b) Compute the standard deviation, range and coefficient of variation from the sample data for each city. 1 mark (c) Draw a box and whisker plot for the median weekly rents of each city and put them side by side on the same scale so that the prices can be compared. 1mark (d) Compare the box plots and comment on the distribution of the data. 3 of 10 1 mark Question 3 4 Marks The Table below is taken from the Australian Bureau of Statistics website. It provides data on energy use of households - almost all houses use mains electricity but some use additional energy sources such as gas and solar. (You can get the data from Table 1 from the URL: http://www.abs.gov.au/AUSSTATS/abs@.nsf/DetailsPage/4602.0.55.001Mar%202014? OpenDocument.) Missing cells indicate data not published, and totals may be higher since all possibilities may not be listed. The totals are not incorrect.). Based on the information available in the table above (a) What is the probability that an Australian household, randomly selected, uses solar as a source of energy? 1 mark (b) What is the probability that an Australian household, randomly selected, uses mains gas and is located in Victoria? 1 mark (c) Given that a household uses LPG/bottled gas, what is the probability that the household is located in South Australia? 1 mark (d) Is the percentage of Australian households using mains gas independent of the state? 1 mark 4 of 10 Question 4 4 Marks (a) The following data collected from the Australian Bureau of Meteorology Website (http://www.bom.gov.au/climate/data/?ref=ftr) gives the daily rainfall data for the year 2015 in Brisbane. The zero values indicate no rainfall and the left-most column gives the date. Assuming that the weekly rainfall event (number of days in a week with rainfall) follows a Poisson distribution (There are 52 weeks in a year and a week is assumed to start from Monday. The first week starts from 29 December 2014 - you are expected to visit the website and get the daily values which are not given in the table below. Make sure you put the correct station number. Ignore the last few days of 2015 if it exceeds 52 weeks.): (i) What is the probability that on any given week in a year there would be no rainfall? 1 mark (ii) What is the probability that there will be 2 or more days of rainfall in a week? 1 mark (Question 4 continued next page) 5 of 10 (Question 4 continued) (b) Assuming that the weekly total amount of rainfall (in mm) from the data provided in part (a) has a normal distribution, compute the mean and standard deviation of weekly totals. (i) What is the probability that in a given week there will be between 5 mm and 10 mm of rainfall? 1 mark (ii) What is the amount of rainfall if only 13% of the weeks have that amount of rainfall or higher? 1 mark Question 5 4 Marks The following data is taken from the UCI machine learning data repository (https://archive.ics.uci.edu/ml/datasets/Wine+Quality). It lists a few attributes of red wine, randomly sampled from thousands of bottles, which can be classified as of good, medium and poor quality. (a) Test for normality of all the variables separately for good wine using normal probability plot. 2 marks (b) Construct a 95% confidence interval for each of the variables for good wine. 1 mark (c) Find the mean of each of the variables for medium quality red wine. Do the same for the poor quality red wine. 1/2 mark (d) Check if the means calculated for the medium and poor quality red wines fall within the corresponding confidence intervals of the good quality wine. For those attributes whose means lie outside the confidence interval, the attributes are significant in determining the quality. This assumption is, however, partially compromised if the attribute fails the normality test. Identify the significant and non-significant variables, and comment. 1/2 mark Good quality red wine Alcohol 10 9.5 10.5 9.7 9.5 10.5 13 10.3 10.8 10.8 10.5 Residual sugar 1.2 2 1.8 2.1 1.9 1.8 1.2 1.4 2.6 2.6 2.1 Chlorides 0.065 0.073 0.092 0.066 0.085 0.065 0.046 0.056 0.095 0.095 0.054 Total sulfur dioxide 21 18 103 30 35 16 93 24 28 28 19 Density 0.9946 0.9968 0.9969 0.9968 0.9968 0.9962 0.9924 0.99695 0.9994 0.9994 0.998 6 of 10 pH 3.39 3.36 3.3 3.23 3.38 3.42 3.57 3.22 3.2 3.2 3.31 Sulphates 0.47 0.57 0.75 0.73 0.62 0.92 0.85 0.82 0.77 0.77 0.88 Citric acid 0 0.02 0.56 0.28 0.16 0.16 0.08 0.47 0.74 0.74 0.58 12.2 9.2 9.2 10.5 10.2 12.8 12.6 10.5 9.9 10.5 10.6 10.6 11.5 11.5 11.5 11.7 12.2 9.8 12.3 11.7 10.4 10 10 12 11.8 12 10 12.9 13 10.8 11.7 11.8 12.3 11 12.3 11 9.8 11.2 11.6 12.5 11.2 13.4 11.2 1.6 2.2 2.2 2.6 1.8 3.6 6.4 5.6 3.5 5.6 2.5 2.5 3.2 3.2 3.65 2.5 3.4 2.3 2.7 2.95 3.1 5.8 5.8 2.4 4.4 2.4 2.5 1.4 4.2 3 6.7 2.4 2.3 2.1 2.3 2.1 2.2 3.7 2.7 1.7 2.8 5.2 2.8 0.054 0.075 0.075 0.085 0.071 0.078 0.073 0.087 0.358 0.087 0.091 0.091 0.083 0.083 0.121 0.078 0.128 0.082 0.072 0.116 0.109 0.083 0.083 0.074 0.124 0.074 0.096 0.045 0.066 0.093 0.097 0.089 0.059 0.066 0.059 0.066 0.072 0.1 0.077 0.054 0.084 0.086 0.084 106 24 24 33 10 37 13 47 10 47 49 49 59 59 14 38 21 29 34 29 23 42 42 18 15 18 49 88 38 30 19 67 48 24 48 24 29 43 19 27 22 19 22 0.9927 1.00005 1.00005 0.99965 0.9968 0.9973 0.9976 0.9991 0.9972 0.9991 0.9976 0.9976 0.9989 0.9989 0.9978 0.9963 0.9992 0.9997 0.9955 0.997 1 1.0022 1.0022 0.9962 0.9984 0.9962 0.9982 0.9924 1.0004 0.9996 0.9986 0.9972 0.9952 0.9978 0.9952 0.9978 0.9987 1.0032 0.9963 0.9934 0.9998 0.9988 0.9998 7 of 10 3.54 3.07 3.07 3.36 3.2 3.35 3.23 3.38 3.25 3.38 3.34 3.34 3.37 3.37 3.05 3.34 3.17 3.11 3.58 3.24 3.15 3.07 3.07 3.2 3.01 3.2 3.19 3.56 3.22 3.18 3.27 3.28 3.52 3.15 3.52 3.15 2.88 2.95 3.23 3.57 3.26 3.22 3.26 0.62 0.84 0.84 0.8 0.72 0.86 0.82 0.77 1.08 0.77 0.86 0.86 0.71 0.71 0.74 0.74 0.84 1.36 0.89 0.75 0.85 0.73 0.73 1.13 0.83 1.13 0.7 0.82 0.6 0.63 0.82 0.73 0.56 0.9 0.56 0.9 0.82 0.68 0.63 0.84 0.74 0.69 0.74 0.04 0.44 0.44 0.47 0.52 0.46 0.45 0.32 0.68 0.32 0.09 0.09 0.39 0.39 0.66 0.01 0.53 0.54 0.02 0.66 0.66 0.66 0.66 0.53 0.71 0.53 0.31 0.05 0.76 0.66 0.53 0.33 0.03 0.47 0.03 0.47 0.72 0.76 0.49 0.01 0.63 0.67 0.63 11.7 10.8 13.3 13.4 11 11 12 12 10.9 10.8 12.5 10.8 11.4 11.8 11.8 2.8 2.8 2.5 2.6 2.6 2.6 6.55 6.55 1.9 1.8 2.9 1.8 2.8 2.4 2.4 0.08 0.081 0.055 0.052 0.07 0.07 0.074 0.074 0.078 0.077 0.072 0.075 0.084 0.107 0.107 17 67 25 27 16 16 76 76 24 22 26 21 43 15 15 0.9964 1.0002 0.9952 0.995 0.9972 0.9972 0.999 0.999 0.9976 0.9976 0.9968 0.9976 0.9986 0.9973 0.9973 3.15 3.32 3.34 3.32 3.15 3.15 3.17 3.17 3.18 3.21 3.16 3.25 3.04 3.09 3.09 0.92 0.92 0.79 0.9 0.65 0.65 0.85 0.85 1.04 1.05 0.78 1.02 0.68 0.66 0.66 0.56 0.55 0.5 0.51 0.53 0.53 0.73 0.73 0.47 0.42 0.63 0.46 0.75 0.64 0.64 Medium quality red wine alcohol 9.4 9.8 9.8 9.4 9.4 9.4 10.5 9.2 10.5 9.9 9.1 9.2 9.2 9.3 9.7 9.5 9.4 9.3 9.5 9.5 9.4 residual sugar 1.9 2.6 2.3 1.9 1.8 1.6 6.1 1.8 6.1 1.6 1.6 3.8 3.9 1.7 2.3 1.6 2.3 1.4 1.8 1.6 1.9 chlorides total sulfur dioxide 0.076 0.098 0.092 0.076 0.075 0.069 0.071 0.097 0.071 0.089 0.114 0.176 0.17 0.368 0.082 0.106 0.084 0.08 0.08 0.106 0.08 34 67 54 34 40 59 102 65 102 59 29 145 148 56 71 37 67 23 11 37 35 density 0.9978 0.9968 0.997 0.9978 0.9978 0.9964 0.9978 0.9959 0.9978 0.9943 0.9974 0.9986 0.9986 0.9968 0.9982 0.9966 0.9968 0.9955 0.9962 0.9966 0.9972 8 of 10 pH 3.51 3.2 3.26 3.51 3.51 3.3 3.35 3.28 3.35 3.58 3.26 3.16 3.17 3.11 3.52 3.17 3.17 3.34 3.28 3.17 3.47 sulphates 0.56 0.68 0.65 0.56 0.56 0.46 0.8 0.54 0.8 0.52 1.56 0.88 0.93 1.28 0.65 0.91 0.53 0.56 0.59 0.91 0.55 citric acid 0 0 0.04 0 0 0.06 0.36 0.08 0.36 0 0.29 0.18 0.19 0.28 0.31 0.21 0.11 0.16 0.24 0.21 0 10.1 9.8 9.2 10.5 10.5 10.3 9.5 9.2 9.5 9.2 9.2 9.2 9.4 9.5 9.6 9.4 10 9.2 9.3 9.8 10.9 10.9 9.6 10.7 10.7 9.5 9.5 9.6 10.5 10.5 10.1 9.2 9.4 9.1 9.4 2.4 2.3 1.8 5.9 5.9 2.2 1.8 2.2 1.6 1.6 1.4 1.7 3 3.8 3.4 5.1 2.3 2.2 1.8 2 4.65 4.65 1.5 1.6 2 2.1 1.9 2.5 2.2 2.2 2 1.6 1.9 2 1.8 0.089 0.083 0.103 0.074 0.074 0.069 0.05 0.114 0.113 0.066 0.074 0.074 0.081 0.084 0.07 0.111 0.076 0.079 0.115 0.081 0.086 0.086 0.079 0.076 0.074 0.088 0.084 0.094 0.093 0.093 0.086 0.069 0.464 0.086 0.401 82 113 50 87 87 23 11 114 37 12 96 23 119 45 10 110 54 52 112 54 11 11 39 15 65 96 94 83 42 42 80 15 67 73 51 0.9958 0.9966 0.9957 0.9978 0.9978 0.9968 0.9962 0.997 0.9969 0.9958 0.9954 0.9971 0.997 0.9978 0.9971 0.9983 0.9975 0.998 0.9968 0.9966 0.9962 0.9962 0.9968 0.9962 0.9969 0.9962 0.9961 0.9984 0.9986 0.9986 0.9958 0.9958 0.9974 0.997 0.9969 3.35 3.17 3.38 3.33 3.33 3.3 3.48 3.25 3.25 3.34 3.32 3.15 3.2 3.34 3.04 3.26 3.43 3.44 3.21 3.39 3.41 3.41 3.42 3.44 3.28 3.32 3.31 3.28 3.54 3.54 3.38 3.41 3.13 3.36 3.16 0.54 0.66 0.55 0.83 0.83 1.2 0.52 0.73 0.58 0.56 0.58 0.74 0.56 0.53 0.63 0.77 0.59 0.64 0.71 0.57 0.39 0.39 0.58 0.58 0.79 0.48 0.48 0.82 0.66 0.66 0.52 0.56 1.28 0.57 1.14 0.07 0.12 0.25 0.36 0.36 0.22 0.02 0.43 0.52 0.23 0.37 0.26 0.36 0.04 0.57 0.12 0.18 0.4 0.49 0.05 0.05 0.05 0.11 0.07 0.57 0.23 0.22 0.54 0.64 0.64 0.12 0.2 0.7 0.47 0.26 pH 3.25 3.16 sulphates 0.57 0.63 citric acid 0.66 0.49 Poor quality red wine alcohol 9 8.4 residual sugar 2.2 2.1 chlorides 0.074 0.2 total sulfur dioxide 47 16 density 1.0008 0.9994 9 of 10 10.7 9.9 11 10.9 9.8 10.2 9.95 9 9.8 9.3 13.1 9.2 9.1 10.5 9.4 9.2 9 9.1 11.4 10.4 9.4 9.8 9.6 9.6 10 10 11.3 11 11 9.6 9.7 11.2 11.4 10.9 9.9 4.25 1.5 3.4 2.1 1.2 5.7 1.8 4.4 1.5 2.8 2.1 2.1 1.5 1.4 3.4 1.3 1.6 1.8 2.1 2 2 3.3 4.5 2.1 2.3 2.1 3.4 2.2 4.4 2.6 1.6 3.1 2.1 2.5 1.6 0.097 0.145 0.084 0.137 0.267 0.082 0.078 0.086 0.172 0.088 0.054 0.084 0.08 0.045 0.61 0.072 0.072 0.058 0.061 0.089 0.087 0.096 0.07 0.07 0.103 0.088 0.105 0.07 0.096 0.073 0.078 0.086 0.102 0.058 0.147 14 48 11 9 29 14 12 29 19 46 65 43 119 85 69 20 42 8 31 55 67 61 49 47 14 23 86 14 13 84 14 12 7 9 51 0.9966 0.99832 0.99892 0.99476 0.99471 0.99808 0.996 0.9974 0.994 0.9976 0.9934 0.9976 0.9972 0.9938 0.9996 0.9965 0.9956 0.9972 0.9948 0.99745 0.99565 1.00025 0.9981 0.9991 0.9978 0.9962 1.001 0.9967 0.997 0.9972 0.998 0.9958 0.99462 0.99632 0.99836 10 of 10 3.63 3.38 3.48 3.5 3.32 3.4 3.55 3.38 3.5 3.26 3.9 3.31 3.16 3.75 2.74 3.17 3.37 3.36 3.51 3.31 3.35 3.6 3.05 3.3 3.34 3.26 3.43 3.32 3.41 3.32 3.29 3.54 3.44 3.38 3.38 0.54 0.86 0.49 0.4 0.51 0.52 0.63 0.5 0.48 0.51 0.56 0.53 1.12 0.48 2 1.08 0.48 0.33 0.43 0.57 0.6 0.72 0.57 0.56 0.52 0.47 0.64 0.58 0.57 0.7 0.54 0.6 0.58 0.55 0.86 0 0.42 0.02 0 0 0.05 0.02 0.08 0.09 0.3 0.15 0.26 0.2 0.04 1 0.02 0.03 0.03 0.06 0.36 0.04 0 0.49 0.49 0.24 0.27 0.22 0.01 0.02 0.48 0.04 0.1 0.24 0.07 0.44