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Title: One Sample t-Test Using MINITAB
Author: Keith M. Bower
Publication Source: Minitab Inc., Keeping TAB #33, February 2000

Abstract

Certain assumptions behind the one-sample t-test are discussed, and an example illustrates the practical interpretations of the results. The linkage between the p-value and confidence interval (CI) results is also mentioned. In particular, the example addresses:

(a) Anderson-Darling Normality test
(b) One-Sample t-test results
(c) P-value from the One-Sample t-test
(d) CI results

Notes

This is a relatively short paper, detailing the key points for performing the one-sample t-test. A side-issue was to discuss the origin of the pseudonym “Student” as I had come across some confusion with practitioners who were not aware of the origins. It is, of course, the pseudonym used by William Sealey Gosset. His original paper (1908) that introduced what we now call the t-test is accessible by clicking here.

The relationship between the P-value and a CI is a key issue in this paper, namely that when using this procedure, with a two-sided alternative hypothesis, if the hypothesized value falls outside the CI, the p-value would be less than the advertised rate. For example, if we are using an α = 0.05 significance level and the hypothesized value falls outside the 95% CI, the p-value will be less than 0.05. Conversely, if the p-value is greater than 0.05, the hypothesized value will fall inside the 95% CI.

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