T-test and Degree of Freedom - Assignment Example

A t-test is used to compare population mean with a standard or for comparing the means of two populations when the population standard deviation is unknown. There is a different t-distribution for each sample size and each is identified by its degrees of freedom (df). The degrees of freedom is the number of independent observations in a sample of data that are available to estimate a parameter of the population (mean and variance) from which that sample is drawn. The precision of the estimate of the population using sample increases as the number of degrees of freedom increases.

As the number of degrees of freedom becomes larger, t-curves look increasingly like the standard normal curve.In normal circumstances, it is not possible to use the entire population to estimate a parameter. Therefore, a sample is drawn from a population that is used to estimate a parameter. There are various reasons for using sample to estimate a parameter instead of population such as the cost of collecting the entire population, time is taken, and availability of entire population. In such cases, population standard deviation is unknown; therefore, z-test cannot be used.

This is why t-test is used most often than z-test.