by Step step procedure to work out Expected Value
(EV) and Standard Error (SE) of the PERCENTAGE
of the values of a sample.
1st step How to recognize Ill need to calculate the EV and SE in the
first place?
These problems will have to address some questions involving a
sample of a set of values from a population. If the question is about a
single value sampled you will not need EV or the SE for the
percentage of sampled values.
2nd step Focus on defining carefully the box model - or population in question. Making a drawing of it and drawing some typical tickets
or population individuals - is useful.
3rd step Think about the percentage of the box (population) values
and also its standard deviation. See also if you have enough
information to guess the histogram of the boxs values.
4th Try step to find out the size of the sample from the question
(dont confuse it with the size of the contents of the box).
5th step - The expected value of an percentage of a sample is always
the same as the percentage of the box, the standard error for a
sample percentage is always calculated as standard deviation of the
box divided by the square root of the sample size.
6th step - If size of the sample is bigger than 20 and the histogram of
the box is not too skewed, we can invoke the Central Limit Theorem
(CLT) to say that the histogram of the sample percentages will follow
a normal distribution.
At this point you will be able to say the AVERAGE of values of a
sample of size n should follow a normal distribution with a given
center (given by EV) and spread (given by SE).