Answer the following questions for the GreatCuppa data set. Assume that the sample of 250 customers is a random sample from the population of all customers.
a) Use the ‘Data / Data Analysis’ tool to calculate descriptive statistics for the cups per week consumed by the surveyed customers. There is a discrepancy between the median and mean cups per week for these data. Use a histogram to explain this.
b) Calculate a 95% confidence interval for the mean income of all customers whose favourite coffee is Latte.
c) Calculate a 99% confidence interval for the proportion of customers who prefer cappuccino.
d) Calculate a 95% confidence interval for the mean income of all customers who prefer ‘other’.
e) John Arabica has suggested GreatCuppa customers who prefer regular coffee are in a mid to lower income bracket (less than $50,000). You are not willing to accept John’s opinion unless you have strong evidence supporting him. Conduct an appropriate test of hypothesis at the 5% level of significance. Give a clear conclusion regarding John’s speculation.
f) John believes that Greatcuppa appeals equally to married and single customers. Conduct an appropriate test of hypothesis. Be sure to state any assumptions required for your test and give a clear conclusion.
Gerald Black of BlackFly Airline has an exclusive contract to run flights of a four-passenger aircraft to a remote mining center. His contract requires him to fly if there are any passengers wanting to make the trip. His fixed costs per day are $400.00, his fixed costs per flight are $1,200.00, the variable cost per passenger is $25.00, and he charges $850.00 per passenger.
He has tracked the number of passengers who flew with him over the past sixty days. His findings are summarized in the following table:
Number of Passengers 0 1 2 3 4
Number of Days 5 12 15 21 7
Of course, he does not fly on days with zero passengers. Assume that this sample gives a good approximation to his future demand patterns. Let G be the random variable: profit on a future day.
a) Calculate the Expected Value, E[ G ], Variance, 2[ G ] and standard deviation, [ G ], of his future daily profit. [Hint: You can calculate a profit corresponding to each number of passengers. The probabilities of those profits are then determined by the probabilities of the numbers of passengers.]
b) Comment briefly on the profitability and volatility of Gerald’s business
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