One-Sample t-Test

Your sample's mean came out at 5.08 and the target was 5.00. Is that a real difference, or just the wobble you'd expect from a handful of measurements?

The t-statistic answers it by measuring the gap in units of "how much wobble this sample size gives you":

• $\bar{x}$ is the sample mean, $\mu_0$ is the value you're testing against, and $n$ is how many values you have.
• $s$ is the sample standard deviation — the one that divides the squared distances by n - 1.
• $s / \sqrt{n}$ is called the standard error: the typical wobble of a mean built from n values. More values means less wobble, which is why the same gap gets more convincing as n grows.

Task: write one_sample_t(values, mu0) returning [t, dof] — the statistic rounded to 4 decimal places, and the degrees of freedom n - 1 as a plain integer.

• values holds at least two numbers and is never all-identical, so the standard error is never zero.
• A negative t is perfectly normal — it just means the sample mean came in below mu0. Don't take an absolute value.

Roughly: |t| above about 2 starts to look like a real difference rather than noise, though the exact cutoff depends on the degrees of freedom.