Standard Errors and Confidence Intervals
Central Limit Theorem
Even means of samples that are NOT Normally distributed have a distribution that is often very close to the Normal distribution
Standard Error (or the mean)
How precisely the sample mean estimates the population mean.
Why is the mean of a larger sample better than the mean of a smaller sample?
It is a more precise estimate of the underlying population mean. (The distribution of the sample mean becomes more concentrated about mu (the population mean) as the same size increases)
Does standard deviation increase or decrease as the sample size, n, increases?
No The standard deviation simply becomes a better estimate of sigma.
The means of samples of Normally distributed variables do themselves have a ______ distribution.
Normal
What is the difference between Standard Deviation and Standard Error?
SD is a descriptive tool that indicates the dispersion in a sample. Standard Error is an inferential tool, which measures the precision of estimates of the population parameters.
If a variable has a population standard deviation sigma, then the Standard Error of the mean, of sample size n, is... (equation)
Sigma/ square root (n)
Standard Error decreases as the sample size, n, increases because...
The denominator in the ratio [sigma/ square root (n)] gets larger
95% Confidence Interval for mu is also called the ________ _______ (of mu)
interval estimate
The estimate of mu (a population parameter) is based on the value of
m (the sample mean)
95% Confidence Interval for mu is...
m +/- 2 (sigma/ square root (n))
In a distribution of sample means, with a mean m and standard deviation equal to standard error, there is a 95% chance that the sample mean is between...
m +/- 2SE (SE= Standard Error)
In a normal distribution 95% of values lie between...
mu +/- 2(sigma)
The population standard deviation sigma can be estimated by the sample standard deviation, s, so the Standard Error of the mean of sample size n is... (equation)
s/ square root (n)