Final answer:
The sigma factor increases RNA polymerase's affinity for promoter sequences, which allows for correct initiation of transcription in E. coli.
Step-by-step explanation:
The correct statement that describes the role of the E. coli RNA polymerase is c. Sigma factor increases the affinity of RNA polymerase for promoter sequences. The sigma factor (σ-factor) is a crucial component of the RNA polymerase holoenzyme in prokaryotes like E. coli. It's responsible for the specificity of transcription initiation by increasing the RNA polymerase's affinity for certain promoter regions of DNA, allowing it to recognize and bind to these sites appropriately. The core enzyme of RNA polymerase, without the sigma factor, would initiate transcription at random places, producing non-functional mRNA. Therefore, the sigma factor is essential for the correct initiation of transcription, allowing the RNA polymerase to correctly transcribe genes into RNA.