Final answer:
DNA ligase is the enzyme most likely to be mutated if the joining of Okazaki fragments is impaired during DNA replication, as it is responsible for sealing the gaps between these fragments.
Step-by-step explanation:
The enzyme most likely to be mutated in the given scenario, where the joining together of Okazaki fragments is impaired, is DNA ligase. Okazaki fragments are short stretches of DNA found on the lagging strand during DNA replication. DNA ligase is responsible for joining these Okazaki fragments together to form a continuous DNA strand.
DNA polymerase I plays a role in this process by removing the RNA primers that were initially placed to start the replication on the lagging strand, and then it fills in the place with DNA nucleotides. However, DNA ligase is the specific enzyme that creates the final phosphodiester bond between the fragments, thereby completing the synthesis of the lagging strand.