One-Sample t-Test

A one-sample t-test is often used the compare the means (or statistic) of a sample against that of a hypothetical mean (or statistic).

Example

A paint manufacturer claims that their paint dries in 15 minutes on average. To test this claim, we bought 30 cans of their paint and found that within this sample, the average drying time was 16 minutes with a standard deviation of 1.5 minutes.

If it can be assumed that our data constitutes a random sample from a normal distribution, does our test tend to support or refute the manufactuer’s claims?

Determine the t-Value

Using the information provided, we can calculate the t-value.

\begin{align} t & = \frac{\bar{x} - \mu}{s\;/ \sqrt{n}}
& = \frac{16 - 15}{1.5\;/ \sqrt{30}}
& = \frac{1}{0.2739} \ & \approx 3.65 \end{align}

Evaluate the t-Value

Using a t-value calculator, we can determine the probability that t will exceed 3.65. In our example, there is a 0.05% chance that we obtain such a result. As this is such a low probability, it is highly probable that we can refute the manufacturer’s claims.