STAT212tdistribution

# STAT212tdistribution - T-distribution The sampling...

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T-distribution- 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 t-distribution has a one-sample t statistic, t= x^-µ/s/√n. There is a different t distribution for each sample size as it has (n-1) 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 bell-shaped. 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 1-n, and 1 is single tailed while 2 is double tailed.) -

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STAT212tdistribution - T-distribution The sampling...

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