Sample Size and Statistical theory - Population Characteristics

Sample Size and Statistical theory - Population Characteristics

Let us assume that we are interested in the attitudes of symphony season ticketholders toward changing the starting time of weekday performances from 8:00 P.M. to 7:30 P.M. The population is comprised of the 10,00C symphony season ticketholders. Their response to the proposal is shown in Figure 12-1. Of these ticket holders, 3000 responded "definitely yes" (which is coded as +2). Another 2000 would "prefer yes" (coded as +1), and so on The needed information is the average or mean response of the population (the 10,000 season ticketholders), which is termed

|x = the population mean = 0.3

This population mean is one population characteristic of interest. It normally is unknown, and our goal is to determine its value as closely as possible by taking a sample from the population.
Another population characteristic of interest is the population variance, a2, and its square root, the population standard deviation, a. The population variance is a measure of the population dispersion, the degree to which the different season ticketholders differ from one another in terms of their attitude. It is based on the degree to which a response differs from the population average response, |x. This difference is squared (making all values positive) and averaged across all responses.1 In our example, the population variance is
a2 = the population variance = 2.22
and a = the population standard deviation =1.49

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