Before exporting, change the sample rate in the lower-left of the Audacity window (Project Rate).
Then, Export
Save as type: Other Uncompressed Formats
Options: Header: RAW (header-less) Encoding: Signed 16-bit PCM
You’ll have to “cross your fingers” for little-endian, because there is no way in Audacity to select the option. When you import a raw file, you can specify little-endian or big-endian, but apparently not when you export.
Is this just a .wav file recorded at a project rate of 8000z?
No. It’s similar to a WAV file but a “raw” file does not have the WAV header. In general, you need special software (that already knows the format details) to play a raw file, because there is no header indicating the format. If you open a raw file in Audacity (or other audio editor) you need to tell Audacity the sample rate, bit, depth, etc.
If open or play a WAV file in place of a raw file, the header will be read as audio and you’ll get a “glitch” in the sound at the beginning of the file. You could also get an offset problem that screws-up the “endiness”, and with the byte-order mixed-up you can get pure-noise.
Just set the “Project Rate” (lower left corner of the main Audacity window) to 8000 before you export, and export as a “normal” (16 bit PCM) WAV file.
If they want a mono file, you will need to ensure that the audio in the project is mono before you export.