In: Statistics and Probability
the z test gives more type I error for small samples compared to t test explain the reason in your own words
answer:
z test:
Z-test alludes to a univariate measurable examination used to test the speculation that extents from two autonomous examples vary significantly. It decides to what degree an information point is far from its mean of the informational index, in standard deviation.
The specialist embraces z-test, when the populace change is known, basically, when there is a vast example estimate, test difference is considered to be around equivalent to the populace fluctuation. Thusly, it is thought to be known, in spite of the way that just example information is accessible thus typical test can be connected.
t test:
A t-test is a theory test utilized by the analyst to think about populace implies for a variable, arranged into two classes relying upon the not as much as interim variable. All the more correctly, a t-test is utilized to inspect how the methods taken from two free examples vary.
T-test pursues t-dissemination, which is fitting when the example estimate is little, and the populace standard deviation isn't known. The state of a t-dispersion is very influenced by the level of opportunity. The level of opportunity infers the quantity of free perceptions in a given arrangement of perceptions.