Applied Statistics 161.111 S1 2024
Assignment 1 Solutions
Total marks: 30
Assessment value: 17%
Background
The population of interest is round cut diamonds for sale in New Zealand.
Data was collected from a random sample of 229 round cut diamonds from a single New Zealand based retailer of diamond jewellery.
The data consists of the price of the diamond (in $NZ), the colour grade (a six point scale from D to I, D being colourless to I being nearly colourless) and the Lab which did the certification of the colour grade (Lab A or B). The data is in the Excel file Diamonds_2024_S1.xlsx
Use the data to answer the following questions in the spaces provided.
Use Excel and incorporate the output into your answers. You can re-size the answer spaces.
When you are finished your assignment, save it as a pdf and upload to Stream Assignment 1 Dropbox
Part A: Exploratory analysis of Colour [6 marks]
A1: Use Excel to produce a table of counts showing the number of diamonds in each colour grade. [2 marks]
A2: Use Excel to draw an appropriate graph to display the table you created above. [2 marks]
A3: What do the graph and table tell you about the number of diamonds in the colour grades? [2 marks]
Part B: Exploratory analysis of price of the diamonds [14 marks]
B1: Use Excel to draw a boxplot of the prices of the diamonds in the sample. [2 marks]
B2: Use Excel to draw a histogram of the prices of the diamonds in the sample. [2 marks]
B3: Use Excel to calculate the numerical summaries of the prices in the sample. Fill in the table with the values rounded appropriately in the column labelled “Price ($NZ)” and the Excel formula you used in the column labelled “Excel Formula Used”. [2 marks]
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Price ($NZ)
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Excel Formula Used
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Mean
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Standard deviation
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Minimum
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Lower Quartile
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Median
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Upper Quartile
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Maximum
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B4: What do your plots and summary statistics tell you about the distribution of diamond prices in the sample? Hint: consider centre, spread, shape and outliers. [4 marks]
B5. Discuss, with justification, whether or not the distribution of the prices of the diamonds is normally distributed? [2 marks]
B6. Identify one other numerical variable that could affect the price of the diamonds and discuss how it would affect the price? [2 marks]
Part C: Confidence interval for mean price of round cut diamonds [10 marks]
C1: Calculate a 95% confidence interval for the mean of round cut diamonds in the population. To get full marks you must show your working for the following: [4 marks]
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Standard error =
Confidence interval =
Lower limit =
Upper limit =
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C2: Write a sentence to interpret your confidence interval in context. [2 marks]
C3: Two conditions (normality of the sampling distribution and representativeness of the sample) need to be satisfied for the confidence interval to be valid.
a) How do we know that the normality condition is met? Explain. [1 mark]
b) Discuss whether the representative condition is met, or not. [2 marks]
C4: A customer sees an advert for a round cut diamond on sale for NZ$6,000. Does your confidence interval suggest that the advertised price is a mistake? Explain. [1 mark]