Question

What is t distribution and how it is related to degrees of freedom?

How is z distribution different from t distribution?

Answer 1

The particular form of the t distribution is determined by its degrees of freedom.

The degrees of freedom refers to the number of independent observations in a set of data.

When we use one sample t test , degrees of freedom = sample size - 1

When we use two sample independent t test, there are different pooled and unpooled degrees of freedom.

When population standard deviation is not known and sample size is small then we use t test, otherwise we use z test.

z distribution looks similar in that it's centered at zero and has a basic bell-shape, but it's shorter and flatter around the center than the z-distribution.The t distribution is very similar to the normal distribution when the estimate of variance is based on many degrees of freedom, but has relatively more scores in its tails when there are fewer degrees of freedom.

The t distribution approaches the normal distribution as the degrees of freedom increase.

The normal distribution is used when the population distribution of data is assumed normal. It is characterized by the mean and the standard deviation of the data. A sample of the population is used to estimate the mean and standard deviation.The t statistic is an estimate of the standard error of the mean of the population or how well known is the mean based on the sample size.