"Student" (real name: W. S. Gossett [1876-1937]) developed statistical methods to solve problems stemming from his employment in a brewery. Student's t-test deals with the problems associated with inference based on "small" samples: the calculated mean (Xavg) and standard deviation (sdev) may by chance deviate from the "real" mean and standard deviation (i.e., what you'd measure if you had many more data items: a "large" sample). For example, it it likely that the true mean size of maple leaves is "close" to the mean calculated from a sample of N randomly collected leaves. If N=5, 95% of the time the actual mean would be in the range: Xavg± 2.776 sdev/N1/2 ; if N=10: Xavg± 2.262 sdev/N1/2 ; if N=20: Xavg± 2.093 sdev/N1/2 ; if N=40; Xavg± 2.023 sdev/N1/2 ; and for "large" N: Xavg± 1.960 sdev/N1/2 . (These "small-sample" corrections are included in the descriptive statics report of the 95% confidence interval.)
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