Assessment details for ALL students Assessment item 2—Assignment 2 for STAT20029 for Term 3, 2016 Due date: Friday 27 Jan 2017, 06:00 pm AEST, Week 10 ASSESSMENT Weighting: 20% 2 General instructions 1. The final mark is out of 20. Questions are from contents covered in Weeks 1-9. 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 a given environment. Full marks will not be awarded to answers which simply demonstrate statistical procedures without comment, interpretation or discussion (as directed in the questions). 2. Reference solutions will be posted to the course website upon release of the marked work. 3. Assignments will receive NO marks if submitted after the solutions are released. 4. This is an individual assignment, which must be submitted online through Moodle. 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: 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 Unit Coordinator through the extension system in Moodle. STAT20029 Statistics for Managerial Decisions Assignment 2, T3 2016 Question 1 4 Marks The table below shows the average daily maximum temperatures at Canberra Airport for 62 days from July 1st to August 31st 2016 (in degree). 13.8 15.8 18.8 16.9 11.8 19.4 11.3 16.4 13.1 19.2 10.4 13.1 14.9 12.1 12.9 15.9 13.9 13.7 12.6 16.7 11.6 13.4 16.1 11.6 8.4 14.1 12.9 14.6 10.6 17.9 10.4 10.7 12.8 13.8 13.2 11.2 15.8 14.4 10.9 16.7 8.4 14.0 7.1 16.2 12.8 13.7 10.1 12.3 13.1 14.9 17.6 14.9 10.2 13.3 8.0 15.6 11.2 18.4 13.1 12.7 11.9 13.7 (a) 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 “less than 10-degree”. 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 “less than 12-degree” (and second be “12 to less than 16-degree”)? 1 mark (d) What proportion of the maximum temperatures were above 16-degree? 1 mark (Note: Use only the original values and not adjusted values.) Question 2 4 Marks The following table (see next page) provides results of customers’ satisfaction survey on four supermarkets in a regional city. This sample data is obtained from a database that contains the similar survey results for different cities in the country. A value of 100 indicates completely satisfactory and a value of 0 means completely dissatisfactory. From this data answer the questions below for the supermarkets. (a) Compute the mean, median, first quartile, and third quartile for each supermarket (do not modify, add to/delete from the table) 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 supermarket. 1 mark (c) Draw a box and whisker plot for the median satisfaction of each supermarket and put them side by side on the same scale so that the satisfaction can be compared. 1 mark (d) Compare the box plots and comment on the distribution of the data. 1 mark Data of customers satisfaction survey on four supermarkets in a regional city Supermarket A Supermarket B Supermarket C Supermarket D 59 70 63 56 60 70 65 58 65 71 65 60 66 71 65 61 70 72 65 61 75 75 66 65 78 77 67 65 80 77 72 65 82 85 73 65 85 89 75 75 90 75 77 77 78 77 79 77 85 78 87 78 79 80 85 87 97 Question 3 4 Marks The table below (see next page) is compiled from Australian Department of Education and Training. It provides data on international student enrolments in Australia in 2015. (https://internationaleducation.gov.au/research/International-Student-Data/Pages/InternationalStudentData2015.aspx). Based on the information available in the table below, (a) What is the probability that an international student, randomly selected, comes from India? 1 mark (b) What is the probability that an international student, randomly selected, comes from Korea and is located in Queensland (QLD)? 1 mark (c) Given that an international student comes from China, what is the probability that the student is located in Victoria (VIC)? 1 mark (d) Is the percentage of international students who come from Vietnam independent of the state? 1 mark International student enrolments in Australia in 2015 (Department of Education and Training) NSW VIC QLD SA WA TAS ACT NT/NAT Total China 65,379 58,064 19,250 12,711 6,987 1,497 6,154 170 170,212 India 16,680 31,758 12,711 3,489 6,139 726 732 269 72,504 Vietnam 9,613 13,181 2,630 1,380 2,123 94 454 100 29,575 Korea 13,663 4,713 6,607 941 1,946 193 603 59 28,725 Thailand 18,491 5,611 2,376 243 888 84 198 74 27,965 Brazil 11,256 2,752 7,102 833 2,628 13 74 14 24,672 Malaysia 4,389 10,455 2,924 1,769 3,549 632 382 23 24,123 Other 103,735 69,270 49,651 10,723 26,224 2,030 4,233 1,543 267,409 Total 243,206 195,804 103,251 32,089 50,484 5,269 12,830 2252 645,185 Question 4 4 Marks (a) The following data (see the next two pages) collected and compiled from investing.com http://www.investing.com/indices/aus-200-historical-data) gives the daily change (in percentage) of S&P/ASX 200 in 51 weeks from Jan 05 to Dec 24 2015. A positive value on a day indicates the stock market moved upwards whereas a negative value means the stock market moved downwards. Assuming that the weekly stock movement (number of days in a week the stock moves either up or down) follows a Poisson distribution (51 weeks and trading only on Monday – Friday each week except public holidays): (i) What is the probability that on any given week over the year the stock market would NOT move upwards? 1 mark (ii) What is the probability that there will be 2 or more days when stock moved upwards in a week? 1 mark (b) Assuming that the weekly total amount of change (in percentage) from the data provided in Q4(a) has a normal distribution, compute the mean and standard deviation of weekly totals. (i) What is the probability that in a given week the total change will be between +0.4 and +2 precents? 1 mark (ii) What is the amount of change if only 2.5% of the weeks have that amount of change or higher? 1 mark Daily change (in percentage) of S&P/ASX 200 in 51 weeks from Jan 05 to Dec 24 2015 1 2 3 4 5 Jan 09 1.56 Jan 16 -0.6 Jan 23 1.51 Jan 30 0.34 Feb 06 0.16 Jan 08 0.52 Jan 15 -0.42 Jan 22 0.49 Jan 29 0.3 Feb 05 0.58 Jan 07 -0.21 Jan 14 -0.95 Jan 21 1.61 Jan 28 0.1 Feb 04 1.23 Jan 06 -1.57 Jan 13 -0.33 Jan 20 -0.03 Jan 27 0.56 Feb 03 1.46 Jan 05 -0.1 Jan 12 -0.37 Jan 19 -0.82 Feb 02 0.42 6 7 8 9 10 Feb 13 2.33 Feb 20 -0.38 Feb 27 0.34 Mar 06 -0.09 Mar 13 -0.61 Feb 12 -0.44 Feb 19 -0.19 Feb 26 -0.61 Mar 05 0.04 Mar 12 0.98 Feb 11 -0.54 Feb 18 0.98 Feb 25 0.3 Mar 04 -0.54 Mar 11 -0.53 Feb 10 -0.25 Feb 17 -0.52 Feb 24 0.32 Mar 03 -0.42 Mar 10 0.05 Feb 09 0.43 Feb 16 0.48 Feb 23 0.27 Mar 02 -0.13 Mar 09 -0.59 11 12 13 14 15 Mar 20 0.41 Mar 27 0.7 Apr 02 0.65 Apr 10 0.61 Apr 17 -1.17 Mar 19 1.86 Mar 26 -1.58 Apr 01 -0.52 Apr 09 -0.48 Apr 16 0.66 Mar 18 Mar 25 0.07 Mar 31 0.78 Apr 08 0.59 Apr 15 -0.64 Mar 17 0.77 Mar 24 0.22 Mar 30 -0.05 Apr 07 0.46 Apr 14 -0.23 Mar 16 0.58 Mar 23 -0.36 Apr 13 -0.14 16 17 18 19 20 Apr 24 1.51 May 01 0.42 May 08 -0.2 May 15 0.68 May 22 0.04 Apr 23 0.12 Apr 30 -0.83 May 07 -0.82 May 14 -0.33 May 21 0.93 Apr 22 -0.59 Apr 29 -1.85 May 06 -2.31 May 13 0.71 May 20 -0.09 Apr 21 0.67 Apr 28 -0.57 May 05 -0.02 May 12 0.88 May 19 -0.77 Apr 20 -0.76 Apr 27 0.83 May 04 0.23 May 11 -0.17 May 18 -1.33 21 22 23 24 25 May 29 1.12 Jun 05 -0.11 Jun 12 -0.21 Jun 19 1.31 Jun 26 -1.54 May 28 -0.21 Jun 04 -1.42 Jun 11 1.42 Jun 18 -1.26 Jun 25 -0.95 May 27 -0.83 Jun 03 -0.93 Jun 10 0.13 Jun 17 1.08 Jun 24 0.04 May 26 0.91 Jun 02 -1.73 Jun 09 -0.49 Jun 16 -0.05 Jun 23 1.32 May 25 1 Jun 01 -0.72 Jun 15 -0.12 Jun 22 0.24 26 27 28 29 30 Jul 03 -1.1 Jul 10 0.39 Jul 17 0.01 Jul 24 -0.43 Jul 31 0.52 Jul 02 1.53 Jul 09 0.03 Jul 16 0.59 Jul 23 -0.43 Jul 30 0.81 Jul 01 1.04 Jul 08 -2 Jul 15 1.05 Jul 22 -1.61 Jul 29 0.71 Jun 30 0.67 Jul 07 1.94 Jul 14 1.9 Jul 21 0.35 Jul 28 -0.09 Jun 29 -2.23 Jul 06 -1.14 Jul 13 -0.34 Jul 20 0.3 Jul 27 0.43 31 32 33 34 35 Aug 07 -2.41 Aug 14 -0.58 Aug 21 -1.4 Aug 28 0.58 Sep 04 0.25 Aug 06 -1.13 Aug 13 0.11 Aug 20 -1.7 Aug 27 1.17 Sep 03 -1.44 Aug 05 -0.42 Aug 12 -1.67 Aug 19 1.45 Aug 26 0.69 Sep 02 0.1 Aug 04 0.33 Aug 11 -0.65 Aug 18 -1.2 Aug 25 2.72 Sep 01 -2.12 Aug 03 -0.35 Aug 10 0.63 Aug 17 0.21 Aug 24 -4.09 Aug 31 -1.07 36 37 38 39 40 Sep 11 -0.47 Sep 18 0.46 Sep 25 -0.58 Oct 02 -1.18 Oct 09 1.33 Sep 10 -2.42 Sep 17 0.94 Sep 24 1.47 Oct 01 1.8 Oct 08 0.24 Sep 09 2.07 Sep 16 1.6 Sep 23 -2.07 Sep 30 2.1 Oct 07 0.59 Sep 08 1.69 Sep 15 -1.53 Sep 22 0.74 Sep 29 -3.81 Oct 06 0.33 Sep 07 -0.2 Sep 14 0.5 Sep 21 -2.02 Sep 28 1.42 41 42 43 44 45 Oct 16 0.73 Oct 23 1.67 Oct 30 -0.52 Nov 06 0.42 Nov 13 -1.45 Oct 15 0.63 Oct 22 0.3 Oct 29 -1.28 Nov 05 -0.94 Nov 12 0.06 Oct 14 -0.11 Oct 21 0.24 Oct 28 -0.2 Nov 04 0.06 Nov 11 0.46 Oct 13 -0.57 Oct 20 -0.65 Oct 27 -0.03 Nov 03 1.42 Nov 10 -0.4 Oct 12 -0.12 Oct 19 -0.21 Oct 26 -0.37 Nov 02 -0.85 Nov 09 -1.14 46 47 48 49 50 Nov 20 0.26 Nov 27 -0.16 Dec 04 -1.46 Dec 11 -0.16 Dec 18 0.09 Nov 19 2.13 Nov 26 0.33 Dec 03 -0.58 Dec 10 -0.84 Dec 17 1.46 Nov 18 0.29 Nov 25 -0.63 Dec 02 -0.15 Dec 09 -0.55 Dec 16 2.42 Nov 17 2.29 Nov 24 -0.95 Dec 01 1.93 Dec 08 -0.91 Dec 15 -0.39 Nov 16 -0.15 Nov 23 0.4 Nov 30 -0.78 Dec 07 -1.14 Dec 14 -0.44 51 Dec 24 1.28 Dec 23 0.49 Dec 22 0.15 Dec 21 0.09 Question 5 4 Marks The following data shows the scores (out of 50) from two student groups (distance and on-campus) from the same examination. (a) Test for normality of the exam scores for the two groups respectively using normal probability plot. 2 marks (b) Assuming an equal population variance to both groups, test if there is a significant difference between the average scores from the two groups on the significance level of α = 0.05?. [Hint: refer to Pages 326-332 in the text] 2 marks Exam scores (out of 50) from distance and on-campus student groups Distance On campus 15 33 14 31 17 33 15 31 19 34.5 15 31 21 35 18 31 24.5 35 21 31.5 25 36 25 32 25 36 25 32 25 37 25 33 27 37 25 33.5 27 37 25 35 27.5 38 25 35 29 43 25 36.5 29 43 25.5 37 29 43 26 37.5 30 43 26 37.5 31 43 26.5 39 31 43 27 40 31 43 27 40 31.5 44 27 41 32 44 27 41.5 32 46 28 42 32 48 28 43 32.5 49 28 43 33 50 30 44 30 45 30 47 30 50