One-sample t-test in R

How to run and interpret a one-sample t-test in R with t.test() — testing whether a sample mean differs from a known value, plus the assumptions to check.

The one-sample t-test answers a focused question: is my group’s mean different from a specific reference value? — a target, a historical norm, a label claim. Here’s how to run and read it in R. (Just want the result from your data? Use our t-test calculator.)

The setup

Say a bag of chips is labelled 50 g. You weigh 20 bags and want to know whether the true mean weight differs from 50.

set.seed(9)
weights <- rnorm(20, mean = 49.2, sd = 2)   # sample data

t.test(weights, mu = 50)

    One Sample t-test

data:  weights
t = -2.5275, df = 19, p-value = 0.02051
alternative hypothesis: true mean is not equal to 50
95 percent confidence interval:
 47.97349 49.80942
sample estimates:
mean of x 
 48.89146 

Reading the output

• t and df: the test statistic and degrees of freedom (n − 1).
• p-value: how surprising this sample mean is if the true mean were 50. Small p → evidence it isn’t 50.
• 95% confidence interval: the plausible range for the true mean. If it excludes 50, the difference is significant at α = .05 — the CI and the p-value always agree.
• sample estimate: the observed mean.

One-sided version

If you only care about underfilling (mean less than 50), use a one-sided test — but decide that before seeing the data:

t.test(weights, mu = 50, alternative = "less")$p.value

[1] 0.01025591

Check the assumption

The one-sample t-test assumes the values are roughly normal (it’s robust for larger n thanks to the central limit theorem). For a small sample, check with a Q–Q plot — see checking normality in R. If normality clearly fails, use the Wilcoxon signed-rank test (wilcox.test(weights, mu = 50)).

And report an effect size alongside the p-value, so readers know how far from 50 you are, not just that it’s “significant.”

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Need this on your own data with assumptions checked and written up? That’s our work.