What is the central limit theorem? What is the standard error of the mean?

Question 5

What is the central limit theorem? Provide examples.

Question 6

What is the standard error of the mean? Provide examples.

Solutions

Expert Solution

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

orchestra answered 1 year ago

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