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The phrase "a test example" is correct and usable in written English.
You can use it when referring to a specific instance or case that is used to illustrate or demonstrate a concept or procedure in a testing context.
Example: "For our experiment, we will use a test example to show how the new software functions under different conditions."
Alternatives: "a sample test" or "an example test case."
Exact(28)
The procedure is illustrated with a test example.
Lid driven cavity flow is computed as a test example.
Finally, for a test example, the TFR analysis of a real life signal is shown.
An office building in Southern China was selected as a test example for energy consumption characteristics.
The performance of the algorithm was checked by a test example.
In a test example, flows most affected were stream seepage and evapotranspiration from groundwater (ETgw).
Similar(32)
I always think of Jean Rhys as a testing example.
A test case example of redesigning an airplane is presented to explore the feasibility of the proposed system.
The problem is always selected as a test case; for example, see [13, 19, 20].
The authors answer the question using the Alzheimer's Disease Neuroimaging Initiative ADNII) as a test case and example.
Compared with the existing validation metrics, the feasibility, effectiveness and efficiency of our proposed two metrics are illustrated by a numerical test example and an engineering example.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com