Uploaded May 2013 | Updated September 2026, 2 hours ago
I work through an example of testing the null hypothesis that the data comes from a binomial distribution. I do this for two tests, one in which the probability of success is specified in the null hypothesis, and one where it is estimated from the data.
Data reference
The Larry Bird free throw data based on information in:
Wardrop, R.L. (1995). Simpson's paradox and the hot hand in basketball. The American Statistician, 49 (1), 24-28.
I work through an example of testing the null hypothesis that the data comes from a binomial distribution. I do this for two tests, one in which the probability of success is specified in the null hypothesis, and one where it is estimated from the data.
Data reference
The Larry Bird free throw data based on information in:
Wardrop, R.L. (1995). Simpson's paradox and the hot hand in basketball. The American Statistician, 49 (1), 24-28.







![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)


