Statistical Estimation and Hypothesis Testing

Statistical estimation is the process of making inferences about a population based on information obtained from a sample. The objective of the estimation is to determine the approximate value of a population parameter on the basis of sample statistic. For example, sample means x are used to estimate population means µ; sample proportions are used to estimate population proportions. Estimation of population parameters may be expressed in following ways in statistical estimation: point estimate and interval estimate

Point estimate: Point estimation of a population parameter provides as an estimate a single value calculated from the sample, this single value is likely to be close in magnitude to the unknown parameter. For instance the sample mean x is a point estimate of the population mean μ and sample proportion p is a point estimate of the population proportion P.

Interval estimate: Interval estimation is defined by two limits (upper and lower limits) between which a population parameter lies. For instance, a < x < b is an interval estimate of the population mean μ which depicts that the population mean is larger than a but lesser than b.

Statistical hypothesis is a method of statistical inference. Statistical hypothesis is an assumption about a population, this assumption does not necessarily true. Hypothesis testing refers to the procedures used by statisticians to accept or reject statistical hypotheses. This procedure used 5~6 steps to come up with conclusion: either the null hypothesis is accepted or rejected (alternative hypothesis accepted) under given/choose level of significance. We accept the hypothesis as being true if it is supported by sample data and reject the hypothesis if sample data fails to support it. Rejection of the hypothesis means that declare it false. This procedure for hypothesis should carefully followed because if the things are overlooked then type I and type II error may occur.