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# ECON1293 - BES Tutorial Sample Solutions S1/11 WEEK 2...

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1 BES Tutorial Sample Solutions, S1/11 WEEK 2 TUTORIAL EXERCISES (To be discussed in the week starting March 7) 1. What is meant by a variable in a statistical sense? Distinguish between qualitative and quantitative statistical variables, and between continuous and discrete variables. Give examples. A variable in a statistical sense is just some characteristic of an ‘object’. It may take different values. Data on a quantitative variable can be expressed numerically in a meaningful way (e.g. height of an individual, number of children in a family. Data on qualitative variables cannot be expressed numerically in a meaningful way; e.g. sex of an individual, hair colour). A discrete quantitative variable can assume only certain discrete numerical values on the number line (can be a finite or infinite number of these values). A continuous quantitative variable can assume any value in a specific range or interval; e.g. length of a pipe. 2. Distinguish between (a) a statistical population and a sample; (b) a parameter and a statistic. Give examples. A statistical population is the set of measurements or observations of a characteristic of interest for all elementary units in a frame; e.g the shoe sizes of all men in Australia. A statistical sample is a subset of a

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2 population; e.g. the shoe sizes of all the men in the class is a sample of the population represented by the shoe sizes of all men in Australia. A parameter is a numerical description of a population. For example, the average shoe size of all Australian men is a parameter (of the population of the shoe sizes of all Australian men). A statistic is a numerical description of a sample. For example, the average shoe size of all men in this class room is a statistic (calculated from the sample of the shoe sizes of all men in this class room). 3. In order to know the market better, the second-hand car dealership, Anzac Garage, wants to analyze the age of second-hand cars being sold. A sample of 20 advertisements for passenger cars is selected from the second-hand car advertising/listing website www.drive.com.au The ages of the vehicles at time of
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ECON1293 - BES Tutorial Sample Solutions S1/11 WEEK 2...

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