stuart pidasso 
 
Please help!!! What is the difference between the t and z distributions? Why is the t used for smaller samples? Is that just the way it is or is there a reason for it? THANKS VERY MUCH!!! 
A little info 
 
When used for sample means, the zdistribution assumes that you know the POPULATION standard deviation (which is never the case). The tdistribution is based on using the sample standard deviation as an estimate of the population standard deviation. Approximating the population standard deviation with a sample standard deviation means the sampling distribution is going to have more spread and is going to be affected by the sample size. Hence for any test statistic value (t=+/2 vs z=+/2) there will be a higher proportion outside those endpoints for the tdistribution. However, as the sample size gets larger the tdistribution approximates the zdistribution. For sample sizes larger than ~25, the difference between the two is usually negligible 
greenliner 
 
Right on and end of story there, from a little info.

stuart pidasso 
 
Thanks for the reply, but I don't understand what you wrote. I am about to blow my head off from this stuff. 
itssimple 
 
z distribution is exact, t distribution is an approximation because you are using a sample to represent the entire population. The bigger the sample size, the closer the t distribution will be to the real distribution. 
26mi235 
 
t is really the "student t" distribution. "z" is not a distribution but when working with the normal distribution it is relatively common to use notation where the variate "z" has a normal distribution (and often normalized, with a mean of zero and a standard deviation of 1). Look at the t value for a given level of "significance" as the number of degrees of freedom increase. You will notice that as the degrees of freedom increase the tdistribution approaches the normal (as stated by others above). Another way to look at it is that when you have a small sample size it is easier to actually have no true effect yet have a measured effect of some size. The higher value of the t statistic for the case of a small sample size compensates for it being easier to get a spurious sample value. 
A little info 
 
Try this website: http://wwwstat.stanford.edu/~naras/jsm/TDensity/TDensity.html It has an applet that lets you change the degrees of freedom (df = n1). It might help. Note: Both the zdistribution and tdistribution are theoretical distributions and therefore both are "exact". They are used to model sampling distributions but are only approximations to any reality. Statistics definitely comes easier to some than to others. If you are having trouble with this, I suggest finding some patient, kind soul in your class that might be willing to spend a few moments with you. While confusing to you right now, they are actually pretty basic. You will find several peers who could probably get you on the right track quickly. Good luck! 
Erbli 
 
Both are theoretical. Both are exact. "...only approximations to any reality." Interesting paragraph. tdistribution: A distribution which is used largely for inferences concerning concerning the mean (or means) of normal distributions whose variances are unknown. Uppercase Z is often called the 'standard normal random variable' with lowercase z being the number of standard deviations separating a (test) value from the mean. Back to you. 
txRUNNERgirl 
 
I just took a test over this stuff this morning. It didn't go well. 