[latexpage]
Population :
The set of all observation of interest. A population is any large collection of objects or individuals, such as Americans, students, or trees about which information is desired.
Parameter:
A parameter is any summary number, like an average or percentage, that describes the entire population.
The population mean µ (the greek letter “mu”) and the population proportion p are two different population parameters. For example:
- We might be interested in learning about µ, the average weight of all middle-aged male of Asians. The population consists of all middle-aged male Asians, and the parameter is µ.
- Or, we might be interested in learning about p, the proportion of likely Indian voters approving of the president’s job performance. The population comprises all likely Indian voters, and the parameter is p.
The problem is that almost 100% of the time yet not 100%, we do not — or can not — know the real value of a population parameter. The best we can do is estimate the parameter! Thus, we need samples and statistics to come in.
Sample:
A subset of observations from the population or a representative group drawn from the population.
Statistic:
A statistic is any summary number, like an average or percentage, that describes the sample.
The sample mean, \(\bar{x}\), and the sample proportion \(\hat{p}\) are two different sample statistics. For example:
- We might use \(\bar{x}\), the average weight of a random sample of 100 middle-aged male Indians, to estimate µ, the average weight of all middle-aged male Indians.
- Or, we might use \(\hat{p}\), the proportion in a random sample of 1000 likely Indian voters who approve of the president’s job performance, to estimate p, the proportion of all likely Indian voters who approve of the president’s job performance.
Because samples are manageable in size, we can determine the actual value of any statistic. We use the known value of the sample statistic to learn about the unknown value of the population parameter.
