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##### Dazzle Jewels Ltd specialises in selling pink diamond jewellery and has been selling

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Question;Dazzle Jewels Ltd specialises in selling pink diamond;jewellery and has been selling only;their proprietary pink diamonds for last 5 years. Pink;diamonds were invented in their;China;laboratories. Their pink diamond sales revenues were reported to have increased;over last 5 years in Singapore. The management is;considering more investment in;marketing for pink diamond jewellery.;Mr. Teo C K, the CEO, has engaged you as a consultant to;advise the management. Since;the 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 management;would like you to study their sales patterns and advise;whether pink diamond jewellery;prices are going up. They would also like to identify what;factors drive prices. A past;industry study indicated that caratage and design complexity;influenced prices. Weight is;measured 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 their;master craftsmen. A sales department report suggested that;customers spent more in city;stores. Dazzle Jewellery management would like to verify if;the above factors do influence;price. Factors should be defined as measurable variables for;statistical analysis and;testing.;Your past studies on other jewellery distribution indicated;that wealth influenced;purchases. Average housing rental data is available and has;been used in past studies as;a 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 2012;and another 100 transactions from year 2013 from each of;their 5 stores. The data is;organised in the excel file;?dazzle_pink_diamonds_student_dataset.xlsx? provided.;Although some members of Dazzle Jewellery management have a;good understanding of;statistical 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 your;inferences, interpretations, conclusions and recommendations;supported by Excel outputs;that validate (or not) the claims mentioned above. The;report should also mention;limitations and concerns if any. An executive summary aimed;at members who are not;knowledgeable in statistics should also be provided.;Variables in Excel Data;Item Auto-generated numbers for 1,000 transaction data;records;Price ($);Price paid;Carat;Weight of the diamonds sold;Year ID;0 for Year 2012 and 1 for Year 2013;Year;Year of the transaction, 2012 or 2013;Style ID;0 for basic machine cut design styles and 1 for complex cut;design;styles;Style;The style of the design, Basic or Complex;Store ID;5 stores numbered 1 to 5;Location ID;0 for residential location and 1 for city location;Location;The location of the store, in a residential or city location;Home Rental ($);The average home rental price per square foot for that area;Your report should include the following;Part I (15 marks);1. For a preliminary investigation to validate if prices of;pink diamond jewellery have;increased, select at least two (2) but not more than four;(4) variables. Explain why you;chose these variables. Describe the data using appropriate;choice of charts. At least;two (2) chart types should be presented. Explain why you;chose these charts.;2. Calculate and interpret measures of location and;dispersion that effectively;describe the data. Can these variables be appropriately;described with the mean and;standard 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 a;randomly selected pink diamond jewel sold is more than 0.18;carats. Define the;probability 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 to;carry 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 a;hypothesis test of the coefficient of correlation.;4. Describe the relationship implied by the model you have;estimated. Execute a;hypothesis 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 in;2012 and 2013. Will the test results affect your;interpretation above? Explain.;2. Determine any other statistical limitations (if any) and;give an explanation of how;they could affect this analysis.;3. Describe possible improvements you would recommend including;data collection;and follow-up analyses.;Part IV (10 marks);1. Describe, discuss & interpret your findings;conclusions, assumptions, limitations and;recommendations for Dazzle Jewellery management in a 300;word executive;summary. You must write concisely.

Paper#61869 | Written in 18-Jul-2015

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