P 288. Class 15. The Central Limit Theorem. Sprigg Lane. Confidence Interval for the mean. If you know and s. There is a 95% p this interval will cover μ . 95% confidence interval for . Standard error goes down with 1/. 2T inv t-value goes down as dof goes up…slowly.
Class 15. The Central Limit Theorem
Confidence Interval for the mean
If you know and s
There is a 95% pthis interval will cover μ.
95% confidence interval for
Standard error goes down with 1/
2T inv t-value goes down as dof goes up…slowly.
Confidence interval gets narrower with n.
In this example, we kept sample mean and sample standard deviation constant.
The first four are LEFT TAIL
The last three are RIGHT TAIL
NPV is a random variable
is a random variable
The mean is
The standard deviation is
Weird and not normal
Close to normal
The distribution is
In selecting simple random samples of size n from a population, the sampling distribution of the sample mean can be approximated by the normal distribution as the sample size becomes large.
Implications of the CLT
If the population (underlying probability distribution) is normal, our tests of hypotheses about means WORK FINE.
If the population (underlying probability distribution) is NOT normal, our tests will still work fine if n is big (>30 is a rule of thumb).