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# Sampling Theory CourseNotes.

Sampling theory is the field of statistics that is involved. with the collection, analysis and interpretation of data gathered. from random samples of a population under study. The application. of sampling theory is concerned not only with the proper. selection of observations from the population that will. A sampling distribution is the frequency distribution of a statistic over many random samples from a single population. Sampling distributions are at the very core of inferential statistics but poorly explained by most standard textbooks.

The sampling distribution, a theoretical distribution of a sample statistic, is a critical component of hypothesis testing. The sampling distribution allows the statistician to hypothesize about what the world would look like if a statistic was calculated an infinite number of times. In statistics, a sampling distribution is the probability distribution, under repeated sampling of the population, of a given statistic a numerical quantity calculated from the data values in a sample. The formula for the sampling distribution depends on the distribution of the. Hence, it is a random variable and its probability distribution is known as its sampling distribution. A point estimator is a formula that uses sample data to calculate a single number a sample statistic that can be used as an estimate of a population parameter. SAMPLING DISTRIBUTION OF THE MEAN. • Sampling distribution of the mean: probability distribution of means for ALL possible random samples OF A GIVEN SIZE from some population • By taking a sample from a population, we don’t know whether the sample mean reflects the population mean.