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Unformatted text preview: As the degree-of-freedom gets larger, the t-distribution gets closer and closer to the standard normal distribution. For practical purposes, the t-distribution is treated as the standard normal distribution when degree-of-freedom is greater than 30. Suppose we have two independent random variable s, one is Z, distributed as the standard normal distribution, while the other has a Chi-square distribution with (n-1) d.f.; then the random variable : (n-1)Z / 2 has a t-distribution with (n-1) d.f. For large sample size (say, n over 30), the new random variable has an expected value equal to zero, and its variance is (n-1)/(n-3) which is close to one. Notice that the t- statistic is related to F-statistic as follow: F = t 2 , where F has (d.f. 1 = 1, and d.f. 2 = d.f. of the t-table) You might like to use Student t-Density to obtain its P-values....
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- Spring '08