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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 $$t = \frac{212 - 250}{39.17 / \sqrt{10}} = -3.07$$.

Example of a One-Sample $$t$$-Test

A researcher tests whether students can accurately estimate a cookie's calorie content, which is known to be 250 calories. A sample of 10 students produces a mean estimate of 212.00 with a standard deviation of 39.17. Using the one-sample t-test formula t = (M − μ₀) / (SD / √n), the calculated t-statistic for this study is ____.

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