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MODULE LBSRE1021: DATA INTERPRETATION MODULE HANDBOOK 2009-10 Copies of lecture presentations, tutorial Excel data and further reading are available using Blackboard Please ensure that you access Blackboard as soon as possible and familiarise yourself with the resources there. MODULE LBSRE1021 DATA INTERPRETATION Essential Text: Oakshott L. (2006), Essential Quantitative Methods for Business, Management and Finance, 3rd ed., Palgrave. (You can use the other editions but chapter numbers may be different.) Students are recommended to study Ch. 1 for revision. Weekly Topic Outlines: 1. Introduction to module - Week Commencing 11th Jan (tut answers available from 21st Jan) Index numbers (Ch.2) 2. Index numbers (cont.) – Week Commencing 17th Jan (tut answers available from 28th Jan) 3. Descriptive statistics: Mean, median, mode, quartiles, standard deviation and use of Excel. (Ch. 6) – Week Commending 25th Jan 4. Probability (Ch 7) – Week Commencing 1st Feb (tut answer available from 11 Feb 2010) 5. Normal distribution. (Ch. 8) - Week Commencing 8th Feb (tut answer week commencing 28th Feb) 6. Directed Study week. 7. Distribution of sample means. Sampling and confidence intervals. (Ch. 9) – Week Commencing 22th Feb 8. Simple hypothesis testing. Test of a population mean. (Z-test and t-test). (Ch. 10) - Week Commending 1st March 9. Chi squared. (Ch. 10) - Week Commending 8th March 10. Correlation and Regression. (Ch. 11) - Week Commending 8th March 11. Revision Assessment: Coursework covering topics 1-2 (50%) 1hr exam covering topics 3-10 (50%) Module LBSRE1021: Data Interpretation Teaching staff contact details: Name Room Tel. ext. (precede by 231 if calling from outside JMU) e-mail Binam Ghimire (Module Leader) 3.18 3592 [email protected] Seng Kiong, Kok 3.13 3844 [email protected] Matthew Veasey 1.52 3447 [email protected] If you need help with the Excel spreadsheet exercises please ask your tutor in the tutorials. Coursework The module is assessed 50% by coursework and 50% by examination. The coursework specification is given in this handbook. It must be handed in to the Aldham Robarts LRC at the time specified. You are strongly advised to commence the assignment in week 2 and complete each section of the assignment immediately following the relevant lectures and tutorials. Late courseworks (except those accompanied by a coursework extension form signed by a year tutor or programme leader) will not be accepted by the Aldham Robarts LRC. You are asked to undertake an analysis of a set of data using the methods covered in the module and the Excel spreadsheet package. You must prepare a word-processed report of approximately 1500 words on your analysis. The 1500 words does not include any graphs, tables of data or figures. The marking scheme for the coursework is given in this handbook. Refer to the marking scheme to ensure that you cover all the required elements of the coursework. LBSRE1021 Assignment 2009-10 This is an INDIVIDUAL assignment. Any instances of COLLUSION or PLAGIARISM will be penalised (see Programme Handbooks for definition of these terms). Briefing Your assignment must be submitted as a hard copy (i.e. on paper and not on disc) and handed in to the Aldham Robarts LRC by 6 pm Monday 22 February 2010 (the Monday after Directed Learning Week). The assignment must be produced using Excel for the calculations and any text must be word processed. Hand written assignments will not be marked. The data is held in the file ‘assign.xls’ which can be accessed from the module Blackboard pages. Your analysis must be undertaken on a part of the data according to the LAST DIGIT OF YOUR STUDENT PERSON NUMBER as stated at the top of the worksheet. Assignments submitted which have used the wrong data set will receive a mark of 0. You are recommended to delete the data which is not assigned to you. The worksheet INDEX contains price and quantity data for 8 products purchased by a company over a 10-year period. Convert these data to Laspeyres' and Paasche's price indices. Present these indices in an appropriate graph. Prepare a report to present your findings. This report should be structured as indicated by the marking scheme on the following page. Note that 25 marks are available for Discussion of your results. Referencing In your assignment, you should ensure that you cite and reference all your sources according to the Harvard convention. If you have doubts about how to use this convention, refer to the on-line guides on the John Moores website. These pages have a link to a more detailed specification of the Harvard system, also accessible through the 'Resources' tab on Blackboard. You should include references to all cited sources in a single list at the end of the assignment. A bibliography should be a single list of all other consulted works placed at the end of the reference list. LBSRE1021 Data Interpretation, Marking Scheme 2010. Report Section Introduction Methods explanation Calculations and Results Discussion Sub Section (1) Title page Contents Introduction text Index Numbers Index Numbers Index Numbers Conclusions Structure & Presentation Sub Section (2) How calculated Examples of practical use Excel Calculations: Laspeyres' Excel Calculations: Paasche's' Graph Increase/ decrease Differences between the calculated Lasp/Paas values Sectioning/ Layout Written quality Referencing Marks 1 1 3 10 10 Sub Total Notes 5 20 10 10 5 10 25 15 25 5 5 5 5 10 Total 20 100 Additionally a number of Graduate Skills have been identified as achievable within this module and the assessments. Subsequently, the below table will be included on your coursework feedback to be included within your portfolio. Graduate Skill Code Skill Description D2 Structures information appropriately with clear introduction and conclusion. D4 Spelling, punctuation, grammar and presentation are of the appropriate standard. G3 Interprets data in charts, tables and graphs and appreciates their importance in displaying data. G5 Recognises patterns and underlying trends in data, and can use them to generalise and interpolate. No skill evidenced Skill evidenced but needs further development Skill well evidenced HELPING YOU LEARN FROM THIS MODULE: The course will be delivered by a lecture followed by a tutorial session which is designed to enable you to solve problems. Some of these problems will be tackled using Excel. You will also interpret and discuss the solutions obtained. Lectures: Each lecture will be delivered by introducing a theme from the module. The lecture will cover key issues for the topic. Learning outcomes will be given at the beginning of each lecture. These are things that you should be able to do once you have completed the session. These learning outcomes are very important since they form the basis of assessment for this module. Reading: At the end of each lecture you will be given directed reading for each session. It is essential that you do purchase and read the recommended text as it supplements the material covered in the lecture sessions. In addition supporting notes are available on the module web pages. Tutorials: Problems are set for each tutorial. It is essential that you prepare thoroughly by considering the lecture material, reading the set text, attempting to solve the set problems and formulating your conclusions based on the results. This will enable discussion of the methods and conclusions in the tutorial sessions. Lively discussion enables students to enjoy the subject and to learn from each other as well as sharpening your own views. Thorough preparation will enable you to be confident and assertive and also stand you in good stead for the assessments. Attendance: The lectures and tutorials are key components of the delivery of this module and if you wish to be successful in your studies it is essential that you attend classes regularly. Registers are to be kept for all tutorials. Please note: You will need a calculator for this module and the examination – a mobile phone is not permitted for use during the exam so please ensure you have a non-programmable calculator for the whole module. Excel Spreadsheet Data Tutorials in weeks 4 and 5 will use Excel to summarise data and produce statistics. You will also be expected to use Excel in your coursework. MODULE LBSRE1021 TUTORIAL Week 2 1. The table below shows three items and the price and quantity purchased by a family during a normal week over a two year period. Item Potatoes Milk Sugar Price 56p/kg 40p/litre 96p/kg 2005 Quantity 3kg 8 litres 1 kg Price 76p/kg 58p/litre 105p/kg 2006 Quantity 3kg 6 litres 2 kg Calculate the Lespeyres' and Paasche's indices for 2006 using 2005 as the base year. 2. A company purchases four items of stationery. The price and quantity of these for 2004, 2005 and 2006 are given below. Item Item A Item B Item C Item D 2004 Price (p) Quantity 16 200 35 600 15 500 10 100 2005 Price (p) Quantity 22 220 33 500 18 400 16 150 2006 Price (p) Quantity 26 300 31 400 20 400 18 200 Calculate the Lespeyres' and Paasche's indices for 2005 and 2006 using 2004 as the base year. MODULE LBSRE1021 TUTORIAL Week 3 1. Use the Excel spreadsheet to solve questions 1 and 2 from tutorial Week 2. 2. The table below shows a company's turnover (£M) and the RPI for a six year period. Year Turnover RPI 1995 30.5 106.3 1996 21.3 110.5 1997 25.2 115.0 1998 29.6 120.7 1999 47.8 136.8 2000 62.5 143.5 Deflate the turnover and plot both the turnover and deflated turnover on a graph using Excel. What conclusions can you draw? MODULE LBSRE1021 TUTORIAL Week 4 (a) 1). Calculate the mean of the following figures: 4, 15, 22, 31, 40, 6, 8, and 42. 2). Find the mode of the following figures: 16, 12, 13, 4, 5, 12, 2, 16, 8, 4, 8, 12, and 5. 3). Find the median of the following figures: 21, 24, 36, 42, 51, 27, 33, 28, 48, 36, and 35. 4). Calculate the standard deviation of the figures in no. 1. 5). Calculate the mean of the following: 41, 25, 62, 34, 78, 64, 21, 23, 43, and 76. 6). Find the mode of the following: 42, 65, 65, 74, 45, 42, 36, 74, 43, 66, 45, 42, and 65. 7). Find the median of the following: 16, 40, 24, 12, 35, 37, 29, 26, 27, and 33. 8). Calculate the standard deviation of the numbers in question 5. 9). Standard Deviation. Exam marks (%) LBSRE1021 P.T. 46 48 54 58 54 LBSRE1021 F.T. 93 21 16 92 38 Calculate the mean and standard deviation for these two sets of exam marks. What conclusions can you draw from these statistics? 10). Answer Question 1 from the past exam papers for May and August 2006 (Available from Blackboard) MODULE LBSRE1021 TUTORIAL Week 4 (b) – This tutorial is a self-study exercise and will not be covered in-class. Calculation of location and dispersion statistics using Excel. 1. Go to the LBSRE1021 module Blackboard pages Go to Lecture 5: Using Excel in Statistical Calculations. Open the Excel data file LBSRE1021.xls. The data concern expenditure (£ spent on one visit) for a sample of 100 supermarket customers. You have to use Excel to calculate the mean, standard deviation and coefficient of variation for the variable. 2. Calculate the Mean: Place the cursor in the cell where you want the mean to appear. The cell immediately below the relevant column of data would be sensible. Select ‘Insert Function’ from the Toolbar (marked fx). Select Statistical for the category and Average from the list of functions. Click OK. You now need to tell Excel which data you to average. Click on the first item in the data column. Hold down the mouse button, drag to the last data item and let go. The column of data should now be surrounded by a dotted line. Click OK. The average should now appear in the cell which you selected. To round the Average to a sensible number of decimal places (say 2): Select Format, then Cells. Select Number, then Number again under Category. Select 0.00 for two decimal places. Click on OK. The Average should now be displayed to 2 decimal places. Alternatively display as UK currency. 3. Calculate the Standard Deviation: Place the cursor in the cell where you want the standard deviation to appear. The cell immediately below the mean would be sensible. Select ‘Insert Function’ from the Toolbar (marked fx). Select ‘Statistical’ from Function Category. Select STDEV for standard deviation. Click OK. Click and drag on the column of data again, then click on Finish. The standard deviation should appear in the cell which you selected. Round this number to 2 decimal places by following the instructions given above. 4. Calculate the Coefficient of Variation. This expresses the Standard Deviation as a % of the Mean. Place the cursor in the cell where you want the Coefficient of Variation to appear. The cell immediately below the standard deviation would be sensible. Enter an appropriate formula (see note 1) into this cell to calculate the standard deviation divided by the mean. Click on the % button (see note 2) to display as a percentage. This is the Coefficient of Variation. 5. Calculate the Median, Quartiles and Mode using a similar procedure to that above but selecting MEDIAN, MODE and QUARTILE from the Paste Function. 6. To the left of the calculated values enter an appropriate key, i.e. Mean Standard Deviation Coefficient of Variation Median 1st Quartile 3rd Quartile Mode You will need to Right Justify these to display them fully. 7. Interpret the statistical calculations. Compare the mean, standard deviations, coefficients of variation, median, quartiles and mode for the variable. What conclusions can you draw? Notes: 1. To enter a formula to calculate the coefficient of variation: You want to divide the s.d. by the mean. You need to know the column letter and row number for these two statistics. Let’s say they are C25 and C24. Click on the cell where you want the result of the formula to be displayed. Type =C25/C24 and Return The result of C25 divided by C24 should now be displayed where you require it. 2. If the % button is not shown you need to display the toolbar. To do this click on the View menu and select Toolbars. Click on the box next to Formatting so that it shows a X and then click on OK. The toolbar with the % button should now be displayed. MODULE LBSRE1021 TUTORIAL Week 5 1. The probabilities that three computer components will need replacing within one year are 1/10, 1/12 and 1/15 respectively. (a) (b) Draw the probability tree Use your tree to find the probability that within one year (i) at least one component will need replacing (ii) no components will need replacing (iii) all three components will need replacing 2. Number of defective items per batch 0 1 2 3 or more Supplier A 500 200 200 100 Supplier B 320 160 80 40 Supplier C 600 100 50 50 (a) (b) (c) (d) (e) If a batch is randomly selected, what is the probability it came from Supplier A, Supplier B, Supplier C. If a batch is randomly selected, what is the probability it contains two defective items? If a batch is randomly selected, what is the probability it would be free from defective items and come from Supplier A? Given that the batch selected came from Supplier B, what is the probability that it contained one or two defective items? If it is known that the batch has two defective items, what is the probability it came from Supplier C? 3. A company is bidding for 2 contracts. The probability that the company will win contract A is 0.4 and the probability that the company will win contract B is 0.7. Use a probability tree to find the probability that the company will (a) win at least one of these contracts (b) win no more than one contract (c) win neither contract (d) win both contracts MODULE LBSRE1021 TUTORIAL Week 7 1. A company packing biscuits knows that the weights are normally distributed about a mean of 500 g with a standard deviation of 5 g. Find the percentage of production which will have weights of:(a) more than 512 g (b) between 506 and 513 g (c) between 488 and 509 g (d) more than 497 g 2. Assuming the hub thickness of a certain type of gear is normally distributed around a mean of 2.00 cm, with a standard deviation of 0.04 cm, find:(a) the percentage of gears which will have a thickness of between 1.95 and 2.06 cm. (b) in a production run of 5,000 gears, how many will have a thickness of more than 1.90 cm? 3. A manufacturer makes chocolate bars with a mean weight of 110 g and a standard deviation of 2 g. The weights are normally distributed. What proportion of the bars are likely to be less in weight than 105 g? The manufacturer decides to make 'bigger' bars with a mean weight of 115 g, but the same standard deviation as before. What proportion of the new bars is likely to be less in weight than the old ones? What mean weight will have to be aimed at if no more than 1 bar in 100 of the new 'bigger' bars is to be less than 115 g in weight? 4. Components made by a certain process have a thickness of 3.00 cm and a standard deviation of 0.03 cm. A component is classified as defective if its thickness lies outside the range 2.96 to 3.05 cm. (a) What proportion of defective components does the process produce? (b) Find the change in the proportion of defective components if the mean thickness is increased to 3.01 cm, with the standard deviation remaining the same. MODULE LBSRE1021 TUTORIAL Week 8 1. If a sample of 100 items is drawn from a population and the mean is found to be 200g with a standard deviation of 5g, find: (a) a 95% confidence interval estimate for the population mean. (b) a 99% confidence interval estimate for the population mean. (c) if a sampling error of only ± 0.5g is allowed, calculate the size of sample which should be selected for parts (a) and (b) of this question. 2. What proportion of samples of size 100, drawn from a population which has a mean of 490g and a standard deviation of 10g, will have means greater than 491g? 3. A random sample of 60 men was found to have a mean height of 170cm and a standard deviation of 5cm. Determine 95% and 99% confidence interval estimates for the mean height of the male population. 4. A firm wants to know the average value of sales invoices. A random sample of 80 sales invoices was selected and found to have a mean of £275 with a standard deviation of £45.50. (a) Find a 95% confidence interval estimate for the population mean invoice value. (b) What size sample should have been selected in order to have a sampling error of only ± £5 at this level? 5. Samples of 100 items are selected at random from a population with a mean of 150g and a standard deviation of 20g. What proportion of samples will have means: (a) between 146 and 156g (b) greater than 148g 6. A manufacturer claims that his products have a mean weight of 500g. A sample of 50 of his products is selected and found to have a mean of 498g with a standard deviation of 6g. Test the validity of the manufacturer's claim. ( Use the 5% level of significance initially) TUTORIAL WEEK 8 CONT. 7. A firm wants to know the average value of sales invoices. A random sample of 100 sales invoices was selected and the mean was found to be £160 with a standard deviation of £22.50. (a) Find a 95% confidence interval estimate for the population mean. (b) Find a 99% confidence interval estimate for the population mean. (c) What size sample should be taken if a sampling error of plus or minus £10 is required at the 95% level? 8. A large supermarket chain took a sample of 100 customer bills during one week and found that the mean was £35.70 with a standard deviation of £6.30. (a) Obtain a 95% interval estimate for the population average shopping bill. (b) What size sample should they take in order to have a sampling error of only £5 at this level? 9. A grocer wants to know whether or not his supplier of bagged potatoes is providing too many bags of incorrect weight. He would be happy if the bags were within plus or minus 100g of the correct weight and he wants to be 99% confident that this is the case. If the initial sample gives a standard deviation of 400g, what size sample would enable him to obtain his required level? 10. Samples of 100 items are drawn at random from a population with a mean of 150g and a standard deviation of 20g. What proportion of samples will have means: (a) greater than 155g (b) less than 148g (c) between 146 and 156g MODULE LBSRE1021 TUTORIAL Week 9 Hypothesis Testing (test of mean using large samples) 1. A street in the city centre has been investigated for the level of traffic noise. The average noise level in the past has always been 130 decibels with a standard deviation of 20 decibels. The residents claim that the noise is getting worse. They take a sample of 50 readings and obtain an average level of 134 decibels. Is their claim justified at the 95% level? 2. A baker, Mr X, makes cakes which he claims have an average weight of 1000g. A shop wishes to buy these cakes and wants to check that the claim for the average weight is correct. They therefore take a sample of 50 cakes and find that their average weight is 950g, with a standard deviation of 200g. Does this result show any significant difference from the baker’s claim for average weight? 3. At the beginning of the year a fast food chain claimed that the average salary earned by its managers will be £18500. Recently, a random sample of 35 managers was taken and their average salary was found to be £16750 with a standard deviation of £3100. Set up a suitable hypothesis and test to see if this sample supports the claim made by the fast food chain. 4. The lifetime of electric light bulbs produced by a given process is normally distributed and is claimed to have a mean of 1500 hours. A batch of 50 was taken and found to have a mean lifetime of 1410 hours. The standard deviation of the sample is 90 hours. Test the hypothesis that the mean lifetime of the electric light bulbs has not changed. MODULE LBSRE1021 TUTORIAL Week 9 Cont. Hypothesis Testing (small samples) 1. After treatment with a standard fertiliser, the average yield per acre is 4.2 tons of wheat. A new fertiliser is administered to 10 acres and the yields are given below. Is this new fertiliser as effective as the standard treatment? Sample yields (tons per acre): 4.3 6.0 4.9 6.1 6.2 5.4 4.1 4.2 3.8 3.9 2. The expected life of electric bulbs is 1500 hours. To test a new batch of light bulbs a sample of 10 was drawn. They had a mean life of 1410 hours and a standard deviation of 90 hours. Test the hypothesis that the new batch has a lower life. 4. A company has been accused of selling underweight products. This product is supposed to weigh 500g. A sample of 6 was weighed and the results were: 495, 512, 480, 505, 490, 502 (g) Is there any evidence that the mean weight is less than 500g? (The weight of the product is known to be normally distributed.) MODULE LBSRE1021 TUTORIAL Week 10 1. A manufacturer produces video recorders at four different factories, A, B, C and D. The reliability of these video recorders is very important to the company. A random sample of video recorders was selected from each of the four factories and tested for reliability. The results of the tests are shown below: RELIABILITY FACTORY A B C D Satisfactory 90 124 92 120 Minor faults found 10 12 16 9 You are required to carry out a suitable test on these results to investigate the possibility that there may be an association between the reliability of the video recorders and the factory at which they are produced. Comment on the usefulness of your results to the manufacturer. 2. Binkshire University is in the process of reviewing the extent to which the degrees offered by its School of Business and Management Studies prepare graduates for the practical aspects of work in a business environment. A random sample of students who graduated from the School over the last five years, and who subsequently gained employment in the business sector, was taken. Each graduate was asked the same question...'How well do you think your degree course equipped you for the work situation?' The results of the survey are tabulated below: TYPE OF DEGREE RESPONSE ACCOUNTANCY MANAGEMENT STUDIES BUSINESS STUDIES Very well 60 45 55 Adequate 34 33 42 Inadequate 16 20 4 Don't know 20 12 9 Test whether or not there is any evidence to suggest an association between the type of degree studied and the response to the question. Use the 5% level of significance initially. Comment on the usefulness of such a test in this case. MODULE LBSRE1021 TUTORIAL Week 11 1. In an agricultural experiment, a newly developed fertiliser was applied at different concentrations to ten identical plots of land. Grass seed was then sown on these plots and, several weeks later, the mean height of the grass on each plot was measured. The results of the experiment are tabulated below: APPLICATION OF FERTILISER (gms per square metre) 10 20 30 40 50 60 70 80 90 100 MEAN HEIGHT OF GRASS (cms) 9.8 11.0 13.2 11.6 14.8 14.8 16.0 19.4 20.6 18.8 Use Excel to (a) Produce a scatter graph to display the information. (b) Find the equation of the regression line for the data and superimpose this line on the scatter graph and calculate the regression coefficient 2. The test department of a major motor manufacturing company can simulate a year's corrosion on car body components in one month under laboratory conditions. The company is investigating the corrosion resistance provided by different thicknesses of paint, and the results of their tests carried out so far are as follows: THICKNESS OF PAINT (mm) 0.25 0.30 0.35 0.40 0.45 0.50 0.55 EQUIVALENT YEARS OF PROTECTION 3.8 5.2 4.6 6.7 6.6 6.9 7.0 Use Excel to (a) Produce a scatter graph to display the information. (b) Find the equation of the regression line for the data and superimpose this line on the scatter graph and calculate the regression coefficient