Step 1: Understanding the Concept:
The choice of an indicator in an acid-base titration depends on the pH at the equivalence point. An indicator is suitable if its color change interval (pKa $\pm$ 1) overlaps with the sharp pH change at the equivalence point.
Step 2: Detailed Explanation:
1. Analysis of Statement I: In a titration between a strong acid (SA) and a weak base (WB), the resulting salt undergoes hydrolysis, making the solution slightly acidic at the equivalence point ($pH<7$). Methyl orange has a working pH range of 3.1 to 4.4, which falls within the acidic range. Thus, it is a suitable indicator. Statement I is true.
2. Analysis of Statement II: Titration of acetic acid (Weak Acid, WA) with NaOH (Strong Base, SB) results in a basic salt (sodium acetate). At the equivalence point, the $pH>7$ due to anion hydrolysis. Phenolphthalein has a working pH range of 8.3 to 10.0, which perfectly overlaps with this basic equivalence point. Therefore, it is a suitable indicator. Statement II is false.
Step 3: Final Answer:
Statement I is true but Statement II is false.