How do you test the nul hypotheses that two samples are equal if only one of the population sizes are known?

The situation appears when you test a measurement instrument by measuring on a certified reference sample with a given nominal value and measurement uncertainty (=standard deviation).

In my case I have made 30 repeated measurements on a certified reference sample , so my own sample size is known.

I have calculated the average and standard deviation of my sample of 30 measurements.

I now want to check the nul hypotheses that the instrument measures correctly versus the alternative hypotheses that they are not equal.

That is, that the mean of my sample is the same as the nominal value of the reference sample vs the alternative hypotheses that they are not equal and the instrument is measuring incorrectly...

How can I do this?

The situation appears when you test a measurement instrument by measuring on a certified reference sample with a given nominal value and measurement uncertainty (=standard deviation).

In my case I have made 30 repeated measurements on a certified reference sample , so my own sample size is known.

I have calculated the average and standard deviation of my sample of 30 measurements.

I now want to check the nul hypotheses that the instrument measures correctly versus the alternative hypotheses that they are not equal.

That is, that the mean of my sample is the same as the nominal value of the reference sample vs the alternative hypotheses that they are not equal and the instrument is measuring incorrectly...

How can I do this?

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