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Inferential Statistics

Satistical Inferences

STATISTICAL INFERENCES

A factory unit producing cars chooses some for inspection and quality check by the quality control department. These cars are chosen randomly for the quality check, form a sample and the totality of the cars manufactured is called the population.

Population: The population is a collection of objects, both animate and inanimate, that is being studied.
Statistical individuals refer to objects in a population. The population can be finite or infinite depending on the number of things in the population.

Sample: A sample is a finite subset of statistical individuals (objects) in a population.
Sampling is a common practice in our day-to-day lives. We use sampling to help us with any statistical inquiry. For example, by analyzing certain samples of specific objects, we may be able to decide whether or not to accept or reject them. The acceptance or rejection of a sample or samples depending on their qualities, on the other hand, results in a sampling error.

Sample Size: The number of statistical individuals (objects) in a sample is called the sample size.

Parameters: The parameters of the population are statistical constants or measures of the population, such as mean(μ), variance(σ2), etc.

Statics: Statistics are statistical measurements or constants computed only from sample observations, such as mean$\left(\overline{)X}\right)$, variance(s2) and so on.

SAMPLING DISTRIBUTION

If we take 50 random samples from a population and calculate their means, we'll end up with a sequence of 50 means that make up a frequency distribution. The sampling distribution of means is the term given to this distribution.
In general, if S1, S2, S3, ...., Sn are values of a static S(mean, variance, etc.) obtained from n independent random samples of a definite size chosen from a given population, then S1, S2, S3, ...., Sn form a sampling distribution of statistics S. The mean ($\overline{)S}$) and variance of statistic S are gi…

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