Tdistribution The sampling distribution of x^ depends on the ∂. When ∂ is unknown we
must use the sampling standard deviation s to estimate the population the standard
deviation, ∂. Supposing we have a SRS of size n from a normally distributed population
with unknown mean µ and sd ∂, the estimated standard error of the statistic is SE= s/√n,
which signifies the variation from one sample to the next.
Thus the tdistribution has a onesample t statistic, t= x^µ/s/√n. There is a different t
distribution for each sample size as it has (n1) degrees of freedom. In general, t(k)
denotes a distribution with k degrees of freedom.
The t distribution resembles that of a standard normal as both are centered at zero,
symmetric, and bellshaped. As the degrees of freedom, k, increase, t(k) approaches the
normal curve (which reflects that s approaches ∂ as sample size increases). However the
differences are that t(k) has an additional parameter, k. Also, t(k) has a larger spread (due
to the random variable s rather than fixed ∂)
Opposite of normsdist in excel [not less than] (c is equivalent to the z value, k is degrees
of freedom which is 1n, and 1 is single tailed while 2 is double tailed.)

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 Fall '10
 JEFFREYHOLT
 Statistics, Normal Distribution, Standard Deviation, TDistribution

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