Can we start a relatively elementary thread about the quality level of a saved .jpg file and its relation to camera resolution settings, if any?

Question

My daughter has thousands of photos shot with a maximum resolution setting on her camera, each one occupying an approximately 4 MB file and apparently capable of generating a quality 32x48 print -- clearly a case of overkill.  I think she's doing it because she thinks it will maximize print quality.  I know it's exhausting our disk space.
In PSE9, I've taken a sample .jpg file (4 MB) and saved it as three .jpg files: at maximum quality (5.2 MB), 50% quality (934 KB), and minimum quality (359 KB).  Note that the minimum quality file represents a 90% reduction in disk space! Then for each of these four sizes, I printed it on letter-size plain paper, and again on 4x6 photo paper.  They looked identical to me.  I asked her to compare them (she did not know which photos had which quality) and with her calibrated eyeballs she thought that the minimum quality was a bit more "pixellated".
I successfully experimented with the editor's "Process Multiple Files" to resize the photos and I am pleased with its performance on my iMac -- less than seven minutes to convert 197 photos.  As a further test,  I ran 5 photos four times: low-quality and high quality, each at 300 dpi and 600 dpi.  Again I saw no apparent difference between 300 dpi low and high quality on letter-size plain paper, but I was taken aback to see the 600 dpi print as approx. 4x6 in the center of the letter-size paper.  I took another look at the four of them in the PSE workplace, and sure enough, the 300 dpi files showed up approximately letter-sized and the 600 dpi files showed up as approximately 4x6.
Obviously I'm dealing with apples and oranges here, and this is why I'd like to see some elementary-level conversation on this subject.

Answer 1

Thanks for the hints, Lundberg. Google led to ImageJ. Rather difficult to understand what it does, but fun to play around with. Further reading led me to this statement:
Another sinusoidal transform (i.e. transform with sinusoidal base functions) related to the DFT is the Discrete Cosine Transform (DCT).
And since jpeg is based on the DCT I thought: simply compressing an image at jpeg and looking at the file size will probably give info re the sharpness of the image. At maximum jpeg setting, there was a significant reduction in file size for a particular image when I applied a Gaussian Blur. So all I have to do is work out how to relate the jpeg file size to the minimum acceptable resolution.
Anyway, thanks for the suggestion.