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To illustrate a one-sample $$t$$-test, suppose a researcher investigates whether students accurately estimate a cookie's calories, known to be $$250$$ (a hypothetical population mean $$\mu_0 = 250$$). The null hypothesis states the population mean estimate $$\mu$$ is $$250$$. From a sample of $$n = 10$$ students, the mean estimate ($$M$$) is $$212.00$$ with a standard deviation ($$SD$$) of $$39.17$$. Using the $$t$$-statistic formula, the score is calculated as $$t = \frac{212 - 250}{39.17 / \sqrt{10}} = -3.07$$.

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