t statistic for an overfilling soda dispenser

Question

A dispenser is supposed to deliver at most $7$ ounces per cup on average. Eight test cups have mean volume $7.1$ ounces and sample standard deviation $0.12$ ounces. Assuming normally distributed volumes and random sampling, what is the value of the appropriate test statistic for checking the claim $\mu=7$ ?

Short answer

$t\approx2.36$ . With a small sample and unknown variance use a one-sample $t$ statistic: $t=\dfrac{7.1-7}{0.12/\sqrt8}=\tfrac{5\sqrt8}{6}\approx2.36$ on $7$ degrees of freedom.

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Maximum Likelihood Estimation: Score and Log-Likelihood
Expectation, Mean, and Variance
Conditional Expectation and Variance Revisited

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