Uploaded July 2013 | Updated September 2026, 2 hours ago
An example of calculating power and the probability of a Type II error (beta), in the context of a two-tailed Z test for one mean. Much of the underlying logic holds for other types of tests as well.
I have a related video with a one-tailed Z test example available at youtu.be/BJZpx7Mdde4.
An example of calculating power and the probability of a Type II error (beta), in the context of a two-tailed Z test for one mean. Much of the underlying logic holds for other types of tests as well.
I have a related video with a one-tailed Z test example available at youtu.be/BJZpx7Mdde4.








![Introduction to the Central Limit Theorem
I discuss the central limit theorem, a very important concept in the world of statistics. I illustrate the concept by sampling from two different distributions, and for both distributions plot the sampling distribution of the sample mean for various sample sizes. I also discuss why the central limit theorem is important in statistics, and work through a probability calculation. (For the most part this is a non-technical treatment, and simply illustrates the important implications of the central limit theorem.)
For those using R, here is the R code to find the probability for the example in this video:
Finding the (approximate) probability that the mean salary of 100 randomly selected employees exceeds $66,000:
1-pnorm(66000,62000,32000/sqrt(100))
[1] 0.1056498
Or, standardizing:
1-pnorm((66000-62000)/(32000/sqrt(100)))
[1] 0.1056498
1-pnorm(1.25)
[1] 0.1056498 Introduction to the Central Limit Theorem](https://i.ytimg.com/vi/Pujol1yC1_A/mqdefault.jpg)

