The t-distribution is also called the Student t-distribution. A Guinness Brewery employee, William Gosset, derived the distribution of T to handle small samples. (Large samples of beer presumably led to less publishable science.) As Guinness did not allow publication of research results at the time, Gosset chose to publish under the pseudonym Student. The journal chosen was Pearsonâ€™s journal, a colleague of Gosset and pioneer of statistics.
Gosset applied his research to a data set containing height and left-middle-finger measurements of 3,000 criminals. These values were written on cards and randomly sorted into 750 samples, each containing four crimi- nals. (This is how simulations were done previously.) The data is available in the Macdonell (HistData) data set.
Run a simulation using 750 samples of size 4. Use quantile to find a 95% confidence interval. Compare to that found with t.test for a single sample of size 4.
As the data is tabulated, youâ€™ll need to expand it: