Customer Account	Customer Type	Total Sales	Stock Code	Total Purchases	Gross Profit Margin	Source Verification	Ethical Score	Satisfaction Score	Brand Loyalty
6585480	P	12,500.00	P9535	8,000.00	36%	N	8	8	8
5497571	P	9,800.00	P54231	7,350.00	25%	N	7	6	7

Variable field value	Description
Customer Account	Represents the unique identifier for a customer.
Customer Type	Represents customer category - 'P' for private customers and 'R' for retailers.
Total Sales	Represents year-to-date sales in Australian dollars.
Stock Code	Represents the identifier for a stock item(s).
Total Purchases	Total cost of goods sold in Australian dollars.
Gross Profit Margin	Represents total sales less total cost of goods sold, expressed in percentage terms.
Source Verification	Represents whether diamond provenance has been verified - 'Y' means provenance has been verified, and 'N' means provenance has not been verified.
Ethical Score	Represents a customer's perception of Louis Edgar's integrity with regards to its conduct and transparency of business practices, and is measured on a 10-point Likert scale ranging from 1 (not ethical) to 10 (highly ethical).
Satisfaction Score	Represents a measure of a customer's experience with their purchase, and is measured on a 10-point Likert scale ranging from 1 (dissatisfied) to 10 (highly satisfied).
Brand Loyalty	Represents a measure of a customer's trust in the brand, and is measured on a 10-point Likert scale ranging from 1 (extreme distrust) to 10 (highly loyal).

F-Test Two-Sample for Variances - Ethical Scores
	Unverified Diamonds	Verified Diamonds
Mean	7.811764706	8.7
Variance	0.487955182	0.281355932
Observations	85	60
df	84	59
F	1.734298539
P(F<=f) one-tail	0.013176198
F Critical one-tail	1.500702791
Variance of variable 1 must > variance of variable 2, which is the case 0.49>0.28.
Otherwise, variables must be swapped.
F>F Critical one-tail (1.73>1.50); hence, Variances are not equal and t-test for
unequal variances should be used.
t-Test: Two-Sample Assuming Unequal Variances - Ethical Scores
	Unverified Diamonds	Verified Diamonds
Mean	7.811764706	8.7
Variance	0.487955182	0.281355932
Observations	85	60
Hypothesized Mean Difference	0
df	142
t Stat	-8.697364008
P(T<=t) one-tail	3.80569E-15
t Critical one-tail	1.655655173
P(T<=t) two-tail	7.61138E-15
t Critical two-tail	1.976810994
(For t-test, the order of variables does not matter)

Task 1: The FD believes that origin-verified diamonds (herein called verified diamonds) are, on average, more profitable than unverified diamonds. He has asked how the data from Louis Edgars management application systems could be examined to test if his understanding is correct. (a) Using the details contained in the dataset, determine which two variables would be best to compare to determine whether verified diamonds are more profitable than unverified diamonds. (b) Identify and justify an inferential statistical method you could use to analyse the profitability of verified diamonds compared to unverified diamonds. (c) Explain how Louis Edgar could use the analysis to inform decision making. You can assume the data follows a normal distribution. You are not required to perform any calculations for this task.