Download Hi, the confidence level when trying to estimate a population mean

Hi,
the confidence level when trying to estimate a population mean from a sample mean
. Well, a very interesting thing, if I'm interpreting it correctly. The Sampling Distribution of the
Mean says roughly that, no matter what the population distribution is - could be just random
numbers with what I call a "flat" distribution - the distribution of the sample means goes to normal
as the sample size increases.
That´s the idea of the Central Limit Theorem
Let X1, X2, X3, …, Xn be a sequence of n independent and identically distributed (iid) random
variables each having finite values of expectation µ and variance s2 > 0. The central limit theorem
states that as the sample size n increases the distribution of the sample average of these random
variables approaches the normal distribution with a mean µ and variance s2/n irrespective of the
shape of the common distribution of the individual terms Xi.
This approximation is exact if X has a normal distribution and it works better with distributions
similar to a normal distribution
If your sample is large enough (not necessarily very large from what I've read) , you can state that
there is a 95% level of confidence that the true mean is within the 1.96 standard deviations of the
population mean. Is this correct?
Yes, the theorem works well for n>30 then the CI for the population mean  is:
CI for the mean  at (1-)% level is x-bar±z(1-/2)s/vn (standard deviation known)
If =0.05 then z(1-0.05/2)=z(0.975)=1.96
CI= x-bar±1.96s/vn
there is a 95% level of confidence that the true mean is within the 1.96 times the standard
deviation of the sample mean (s/vn) of the sample mean
I have two questions about correlations, which are related.
How good a fit are the data points to the regression line, and what is the confidence level that this
regression line can be used to make predictions for different x variables?
The coefficient of determination (R2) it´s a measure of how well fits the regression line to the data
points. Formula:
R2=r2 where r is tha sample correlation
Did you go to the site I sent you?
Yes, I see that
This gives the user a result, based on a z-score conversion, something like the above, the
confidence level that the correlation coefficient is within a certain range of the true r.
The pages computes a confidence interval for rho () but if you want to compute an interval for y
given a particular value of x you must use the prediction confidence interval (the second one of
the above intervals)
But what does this tell me about the level of confidence and range for a projection using a
regression line? Can I say that, when I project an unknown y from x, I can state there is a 95%
chance that the predicted y falls in a certain range?
Use the prediction confidence interval
Can I get something like this from the F-score?
When you use lineEST in excel appears the value of the F-score but if you want to predict an y –
value (not only the value, you want a CI) look at the lower and upper limits