Why does the book say T-distribution is more conservative compared to Z-distribution?
You can see that yourself if you compare 95% significance level of T-distribution for any degree of freedom and Z-distribution. Explanation is that T-distribution has fat tails and therefore higher chance of extreme events than normal distribution.
The interval will be wider, so you are making a more cautious statement. That is, it’s easier to say that the mean will be between 60 to 140, than it is to say it will be between 90 and 100!
As the degrees of freedom approach infinity the T-distribution will approach a normal distribution.
maratikus Wrote: ------------------------------------------------------- > You can see that yourself if you compare 95% > significance level of T-distribution for any > degree of freedom and Z-distribution. Explanation > is that T-distribution has fat tails and therefore > higher chance of extreme events than normal > distribution. I can’t see how is fatter tail linked with conservativeness? Dreary’s explanation is more understandable. Thank you all.
The fatter tail itself is not more conservative. The fatter tail just means that smaller samples tend to have a higher probability of larger deviations from the mean than larger samples. As a result, the range of values in which we can expect a random variable to be located a certain percentage of time must be larger. The T distribution establishes a wider range of values then a normal distribution by establishing a wider interval for a given level of confidence. Because you’re using a wider range with the T distribution it’s more conservative.
it’s very simple: fat tail -> wider confidence interval
So when a graduate student teaches math for the first time, there is always this moment when s/he stands at the front of the classroom and decides “none of them have a clue what I’m talking about”. maratikus needs that moment.
…and the more t get fatter the more became as Z… You should go on diet? t or Z?
…and the more t get fatter the more became as Z… Who should go on diet? t or Z?
strangedays, the less fatter the closer it gets to z.