How does can a z-test and t-test relate to a normal curve?

Question

How does can a z-test and t-test relate to the normal curve?

Why is it important???

Answer 1

In order for the Z-test to be reliable, certain conditions must be met.

It must be known that the population varies normally (i.e., the sampling distribution of the probabilities of possible values fits a standard normal curve). The Z test is generally used when the sample size is large.  T test is used when sample size is small (ie < 30).  

When the area of the standard normal curve is divided into sections by standard deviations above and below the mean, the area in each section is a known quantity. The area in each section is the same as the probability of randomly drawing a value in that range.

In order to use the area of the normal curve to determine the probability of occurrence of a given value, the value must first be standardized, or converted to a z- score. To convert a value to a z-score is to express it in terms of how many standard deviations it is above or below the mean. After the z-score is obtained, its corresponding probability may be looked up in a table.

There are two important reasons to standardize scores.  

1)  Standardized scores allow for comparison of scores from data sets that have different means and standard deviations.  

2) Standardized scores give the exact location of any score in a distribution in relation to the mean.  

i hope that this helps!

ps If all of the above fails to answer your question check out:

http://davidmlane.com/hyperstat/A25329.h...