Saturday, December 18, 2010

When to use the T distribution?

On pg 333, chapter 8, question 22, the sample size is less than 30, the SD is unknown, but in part (B) of the question it says "the population has a normal distribution".

So should you use the T distribution or normal distribution? Go for the T dist because the standard deviation is unknown. So, even if the population is normally distributed, if you don’t know its standard deviation, use the T. In fact I always use the T distribution in applied (real) work. It is safer, giving you a wider margin or error and therefore confidence interval. Therefore the chances of rejecting a true null (and therefore making a Type 1 error are smaller. Nice question, thanks RB.

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