



 
Hi Don, An extremely nice feature of the normal distributions is that any random normal variable X with mean μ and standard deviation σ can be transformed to the standard normal random variable Z by the transformation Z = (X  μ)/σ. A consequence of this is that Pr(0 < X < k) = Pr(0 < (X  μ)/σ < (k  μ)/σ) = Pr(0 < Z < (k  μ)/σ) and hence Pr(0 < X < k) can be evaluated using the standard normal table. There is no similar "standard tdistribution". If X has the tdistribution with 6 degrees of freedom and you want to evaluate Pr(0 < X < k) you need a table for the tdistribution with 6 degrees of freedom. If X has the tdistribution with 8 degrees of freedom and you want to evaluate Pr(0 < X < k) you need a table for the tdistribution with 8 degrees of freedom. There are reference books that have tables of tdistributions for various degrees of freedom but most statistics books have one table with a few values for degrees of freedom from 1 to 30. If you want to find a pvalue where the test statistic has a tdistribution there are two options commonly used. If the degrees of freedom are large (usually over 30) then the tdistribution and standard normal distribution are approximately equal so you can use the standard normal table. A better solution is the one you have found, that is to use software to calculate the pvalue. Harley  


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