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Differences between t-distribution and z-distribution 2009.12.05 Hye-jung Cho t-distribution • • • • The t-distribution has one parameter called the degree of freedom (df), DF=n-1 The t-distribution is similar to the normal distribution: Symmetric about 0 Bell shaped • The main differences between the t-distribution and the normal distribution is in tails (Play around with DF and see the difference of the tails): T-distribution has larger tails than the normal Larger DF means smaller tails, the larger the DF, the closer to the normal distribution Small DF means larger tails • • • z-distribution • Z is normal with mean 0 and standard deviation of 1. Differences between t-distribution and z-distribution • distribution t z population standard deviation unknown unknown sample size Small Large sample distribution Normal fat tails fatter tails (more probability in tails) Peak Less degrees of freedom Smaller distribution critical value (95%, two-tail) 1.98 (100 observations, df=99) z=1.96 As the sample size increases, the t-distribution gets closer to the z-distribution
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