Final answer:
The incorrect statement about Okazaki fragments is that they are longer in eukaryotic cells, as they are actually short stretches of DNA on the lagging strand.
Step-by-step explanation:
The characteristic that is NOT true for Okazaki fragments is that they are longer in eukaryotic cells. Okazaki fragments are short stretches of DNA found on the lagging strand of DNA which is synthesized discontinuously and in the direction away from the replication fork. These fragments do indeed begin with an RNA primer which is later replaced by DNA nucleotides, and they are joined together by the enzyme DNA ligase to form a continuous strand.
DNA polymerase III checks the accuracy of the newly synthesized DNA right after the DNA is synthesized, not specifically the Okazaki fragments, but DNA polymerase I plays a significant role in processing Okazaki fragments by removing the RNA primers and replacing them with DNA. Therefore, the correct answer is that they are longer in eukaryotic cells, which is not a characteristic of Okazaki fragments.