Step 1: Understand the topic.
Leather tanning is an everyday use of colloid chemistry. It works because particles with opposite charges pull towards each other.
Step 2: Look at the charge on animal skin.
Animal skin is made of protein. Under tanning conditions this protein behaves as a positively charged colloid.
Step 3: Look at the charge on tannin.
Tannin comes from plants and behaves as a negatively charged colloid.
Step 4: Judge Statement I.
Since skin is positive and tannin is negative, Statement I is correct. The opposite charges let tannin stick to the skin and turn it into leather.
Step 5: Judge Statement II.
Modern industry also uses chromium salts in place of tannin to tan leather. This gives a tougher, better leather, so Statement II is also correct.
Step 6: Combine the judgements.
Both Statement I and Statement II are true.
Step 7: State the final answer.
The correct choice is:
\[ \boxed{\text{Both Statements I and II are correct}} \]