Which formula gives the t-statistic for a one-sample t-test?

t = \frac{\bar{x} - \mu}{s/n}

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t = \frac{\bar{x} - \mu}{s/\sqrt{n}}

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t = \frac{\bar{x} - \mu}{s}

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t = \frac{\mu - s}{\bar{x}/\sqrt{n}}

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Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

The t-statistic measures how far the sample mean is from the claimed mean, in standard errors.
The standard error of the mean is $\frac{s}{\sqrt{n}}$ , so $t = \frac{\bar{x} - \mu}{s/\sqrt{n}}$ .

Worth noting

$\frac{s}{n}$ shrinks the standard error too fast; it falls with $\sqrt{n}$ , not $n$ .

Ten questions from Sampling, Inference & the t-Test, at your own pace.

Ten questions from Sampling, Inference & the t-Test, at your own pace.

Explanation