One-Sample Two-Tail t-Test for Mean

193. One-Sample Two-Tail T-Test for Mean

Example

A snack company’s energy bars are labeled as containing 20 grams of protein. A consumer group suspects the actual mean protein content differs from the label — it could be over or under. They take a simple random sample of 31 bars and measure a mean of 21.40 grams with a sample standard deviation of 2.54 grams. Assume protein content is normally distributed. At $𝛼$ = 0.05, test whether the mean protein content differs from the labeled amount.

\begin{aligned} 𝐻_{0} & : 𝜇 = 20 \\ 𝐻_{𝑎} & : 𝜇 \neq 20 \end{aligned}

Since $| 𝑡 | = 3.07 > 2.04$ , reject $𝐻_{0}$ ( $𝑝 \approx 0.0045$ ). There is sufficient evidence at $𝛼 = 0.05$ that the mean protein content differs from 20 grams.