In: Statistics and Probability
Question 5
What is the central limit theorem? Provide examples.
Question 6
What is the standard error of the mean? Provide examples.
What is the central limit theorem? Provide examples
For n>30 large samples.
As sample size increases the distribution tends to be normal with sample mean=xbar=
and sample standard deviation=s=
Example:
Take a simple random sample szie 144 from a population with mean 240 and standard deviation=18
According to central limit theorem,the approxiamte sampling distrubtion of sample mean is normal with sampl mean
=xbar=mu=240
sample standard deviation=sigma/sqrt(n)=18/sqrt(144)=18/12=1.5
What is the standard error of the mean? Provide examples.
standard error of sample mean=
Standard error of mean=SE==sigma/sqrt(n)=18/sqrt(144)=18/12=1.5