Marycarol,
As an engineer, I want to comment on my understanding of CT vs. Sputum.
A CT is quick, but subjects you to a lot more radiation than a simple Chest XRay. That is why they try to limit CTs to two/year, or maybe four.
The results can come back the same day, but it's a subjective interpretation by a human. There has been some research with computers evaluating the XRays, and the results are promising. However, XRays are limited in their resolution. A ball park number would be about 1mm or 0.039 inches.

For some people, it's very difficult to get a sputum sample; with an XRay, you just lie there. Easy. After you get three sputum samples, they have to be "good" samples. I had one that had too much saliva in it, so only
two of the samples could be processed. Then you have to wait 4-6 weeks for the lab to grow the stuff. Some labs are better than others. You might get a negative reading, even though a little bit of MAC is present.
However, if you get two positives, you definitely have MAC.
So a doctor should use XRays to keep an eye on you, and if the XRay indicates you might have MAC, then the sputum test would be appropriate.

A yes or no result is based on two different scientific principles, so both are useful.

Harry