The owner of a large fleet of taxis is trying to estimate his costs for next year’s operations. One major cost is fuel purchases. To estimate fuel purchases, the owner needs to know the total distance his taxis will travel next year, the cost of a gallon of fuel, and the fuel mileage of his taxis. The owner has been provided with the first two figures (distance estimate and cost of a gallon of fuel). However, because of the high cost of gasoline, the owner has recently converted his taxis to operate on propane. He has measured and recorded the propane mileage (in miles per gallon) for 50 taxis
a) what is the population of interest
b) what is the parameter the owner needs
c) what is the sample
d) what is the statistic
e) describe briefly how the statistic will produce the kind of information the owner wants
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Would the population of interest simply be the overall cost of next year's operation?
The Population of interest is where the data will be collected
E.G. Height of college students in London, the population of interest is the London college students.
This case is slightly odd in the way it could be measuring the price of propane or taxi mileage but I assume the population of interest will be petrol(gas) stations which supply propane fuel.
Population of interest: The fleet of taxis
Parameter:Average Propane mileage of the taxis
Sample: 50 taxis
Statistic: Average propane mileage of the sample (50 taxis)
According to Central Limit Theorem, samples´means follow a normal distribution centered in the true mean of the population and with a Standard Error=Population Standard Deviation/SquareRoot(Sample Size)
In this way we can construct a confidence interval based on a significance level (alpha) for the fleet average propane mileage. We can estimate the mean with a certain confidence level (1-alpha)