One-Sample t-test, Visually Explained

Introduction to one of the most famous statistical tests

William Sealy Gosset (1876–1937) known as Student (image from public domain hosted on wikipedia)

The one-sample t-test is a statistical test used to determine whether the mean of a single sample of data is significantly different from a known or hypothesized value. It is a common test used in inferential statistics to draw conclusions about a population based on a sample of data.

The basic idea behind the one-sample t-test is to compare the sample mean to a hypothesized population mean, and determine whether the difference between the two is large enough to be statistically significant. The test assumes that the data are normally distributed and that the population variance is unknown but can be estimated from the sample.

Typical applications of the one-sample t-test include:

1. Testing whether a sample mean is significantly different from a known value, such as the population mean or a hypothesized value based on theory or previous research.
2. Comparing the effectiveness of a new treatment or intervention to a known or established standard.
3. Testing whether a process or system is operating within acceptable limits by comparing the observed mean to a specified target value.
4. Evaluating the accuracy of a measuring instrument by comparing…