Question

1. For a t distribution with k degrees of freedom, (t(k)), what does this distribution approach as k increases? Why?

2. How do t distributions help one to analyze samples from normal distributions?

Answer 1

1. As df increases(here df is k), the t dist approaches to normality.. This means that the area near the center increases while area near the tails decreases. When df decreases, the area near the center decreases while the area near the tails increases...this is the reason that's why t tends to normal as K increases...

2.normal distribution is used when the population dist of data is assumed normal. .. The tstat

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.

In this way t dist help one to analyze

samples from normal distributions

Note-if there is any understanding problem regarding this please feel free to ask via comment box..thank you