What would be a statistical test that one could use to determine whether a gene is significantly expressed (that is, above background/experimental noise) in a cell or cell population?
The data in question is a single cell RNA sequencing data set of a mouse brain. All appropriate normalization and quality control measures have already been completed. I am interested in a particular gene and, when querying the expression of that gene, I am able to identify only 107 out of ~300,000 cells which show any detected transcript. Moreover, in those cells, the UMI count is 1 - 2. Finally, these cells do not clearly segregate based on other characteristics (e.g. cell type) or cluster together when visualized using dimensionality reduction. Thus, I am almost certain that this is mere background noise and my gene of interest is not expressed at all within this mouse brain.
However, how would I statistically answer this question?