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Statistics - Dazzle Jewels Ltd Assignment Solution

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Question;Dazzle Jewels Ltd specialises in selling pink diamond jewellery and has been selling onlytheir proprietary pink diamonds for last 5 years. Pink diamonds were invented in theirChina laboratories. Their pink diamond sales revenues were reported to have increasedover last 5 years in Singapore. The management is considering more investment inmarketing for pink diamond jewellery.Mr. Teo C K, the CEO, has engaged you as a consultant to advise the management. Sincethe official opening of their first store in 1st June 2003, they have opened five (5) stores.Stores were located in the city and in residential estates. Dazzle Jewellery managementwould like you to study their sales patterns and advise whether pink diamond jewelleryprices are going up. They would also like to identify what factors drive prices. A pastindustry study indicated that caratage and design complexity influenced prices. Weight ismeasured in carats. Dazzles only offer two categories of design styles, basic and complex.The basic styles are cut by automated machines. Complex designs are produced by theirmaster craftsmen. A sales department report suggested that customers spent more in citystores. Dazzle Jewellery management would like to verify if the above factors do influenceprice. Factors should be defined as measurable variables for statistical analysis andtesting.Your past studies on other jewellery distribution indicated that wealth influencedpurchases. Average housing rental data is available and has been used in past studies asa proxy for the wealth. You have asked Dazzle Jewellery to randomly collect data on price,year of transaction, carats, design complexity, location, and average housing rental.Dazzle Jewellery randomly selected 100 transactions of pink diamonds from year 2012and another 100 transactions from year 2013 from each of their 5 stores. The data isorganised in the excel file ?dazzle_pink_diamonds_student_dataset.xlsx? provided.Although some members of Dazzle Jewellery management have a good understanding ofstatistical models and methods, most of the members have only a basic understanding.Use Excel software to analyse data to write a report. Your report should include yourinferences, interpretations, conclusions and recommendations supported by Excel outputsthat validate (or not) the claims mentioned above. The report should also mentionlimitations and concerns if any. An executive summary aimed at members who are notknowledgeable in statistics should also be provided.Variables in Excel Data:Item Auto-generated numbers for 1,000 transaction data recordsPrice ($)Price paidCaratWeight of the diamonds soldYear ID0 for Year 2012 and 1 for Year 2013YearYear of the transaction, 2012 or 2013Style ID0 for basic machine cut design styles and 1 for complex cut designstylesStyleThe style of the design, Basic or ComplexStore ID5 stores numbered 1 to 5Location ID0 for residential location and 1 for city locationLocationThe location of the store, in a residential or city locationHome Rental ($)The average home rental price per square foot for that areaYour report should include the following:Part I (15 marks)1. For a preliminary investigation to validate if prices of pink diamond jewellery haveincreased, select at least two (2) but not more than four (4) variables. Explain why youchose these variables. Describe the data using appropriate choice of charts. At leasttwo (2) chart types should be presented. Explain why you chose these charts.2. Calculate and interpret measures of location and dispersion that effectivelydescribe the data. Can these variables be appropriately described with the mean andstandard deviation? Explain.3. Population mean and standard deviation are given as 0.14 and 0.04 respectively.Using a normal distribution, identify and compute the probability that the weight of arandomly selected pink diamond jewel sold is more than 0.18 carats. Define theprobability that the weight is exactly 0.18 carats. Explain the difference.Part II (20 marks)Apply a suitable hypothesis-testing approach to analyse the factors that drive price.1. State and explain your hypothesis. Explain how regression analysis can be used tocarry out this test.2. Identify and fit a suitable linear regression model to the data. List your variables.3. Interpret the relevant statistics from the output generated by your Excel software.Statistics should include the coefficient of correlation, coefficient of determination and ahypothesis test of the coefficient of correlation.4. Describe the relationship implied by the model you have estimated. Execute ahypothesis test on each of the regression coefficients in your model and interpret.5. Discuss if the assumptions of the models used are valid for the data.Part III (15 marks)1. Use an ANOVA test to evaluate if the prices among the 5 stores are the same in2012 and 2013. Will the test results affect your interpretation above? Explain.2. Determine any other statistical limitations (if any) and give an explanation of howthey could affect this analysis.3. Describe possible improvements you would recommend including data collectionand follow-up analyses.Part IV (10 marks)1. Describe, discuss & interpret your findings, conclusions, assumptions, limitations andrecommendations for Dazzle Jewellery management in a 300 word executivesummary. You must write concisely.

 

Paper#61816 | Written in 18-Jul-2015

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