This problem led him to “discover” what is called the Student’s t-distribution. He realized that he could not use a normal distribution for the calculation he found that the actual distribution depends on the sample size. Just replacing σ with s did not produce accurate results when he tried to calculate a confidence interval. His experiments with hops and barley produced very few samples. Goset (1876–1937) of the Guinness brewery in Dublin, Ireland ran into this problem. A small sample size caused inaccuracies in the confidence interval. However, statisticians ran into problems when the sample size was small. They used the sample standard deviation s as an estimate for σand proceeded as before to calculate a confidence interval with close enough results. In the past, when the sample size was large, this did not present a problem to statisticians. In practice, we rarely know the population standard deviation. Discriminate between problems applying the normal and the Student’s t distributions.
Interpret the Student’s t probability distribution as the sample size changes.
