t-Distribution

t-Distribution
l In biological research the population variance is usually unknown and an
unbiased estimate s2, obtained from the sample data, has to be used in
place of ?2.
l The properties of t- distribution are:
l 1-It is symmetrical about the mean.
l 2-It is really family distributions, which depend on the degrees of freedom
(df), of samples.
l 3-It is not normal distribution and it approach to normal as ( n ) approaches
infinity.
l 4-t curve is somewhat flatter than that for standardized normal distribution.
l 5-It has a mean zero and variance more than one but it approaches one as
the sample size become large.
Note: When the sample n > 30, our faith in (s) as an
approximation of (s) is usually substantial, and we may feel
justified in using normal distribution theory to construct
confidence interval.
l Confidence Interval for the Difference between Two
Population Means ?1 and ?2; When ?1 = ?2 but are unknown,
(C.I);
l
l A (1- a) 100% confidence interval for ?1 - ?2 is given by,