Step 1: What we must judge.
Two statements are given about Entamoeba histolytica, the parasite that lives in the human gut. We check each one for truth.
Step 2: Check statement I.
Statement I claims the parasite is a facultative anaerobe because it has mitochondria. This is wrong. Entamoeba histolytica actually lacks normal mitochondria. It lives in the low-oxygen gut and survives without oxygen, so the reasoning about mitochondria is false. So statement I is false.
Step 3: Check statement II.
Statement II says it causes abscesses in the wall of the large intestine. This is true. The parasite invades the lining of the large intestine and produces ulcers and abscesses, the disease known as amoebiasis or amoebic dysentery. So statement II is true.
Step 4: Combine the verdicts.
Statement I is false and statement II is true. This matches option 4.
Step 5: Why other options fail.
Options saying both are true, both are false, or only I is true all contradict our findings, so they are rejected.
Step 6: Conclusion.
Therefore the correct answer is "Statement I is false. But II is true". \[ \boxed{\text{I false, II true}} \]