Snitzelhoff wrote,
"Then he called for a light, and sprang in, and came trembling, and fell down before Paul and Silas, and brought them out, and said, Sirs, what must I do to be saved? And they said, Believe on the Lord Jesus Christ, and thou shalt be saved, and thy house."--Acts 16:30-31
The question was directly asked. It was directly answered. There are a host of other passages that say much the same thing, but I consider that passage sufficient for the fact that the question was directly asked and directly answered.
I see that you very conveniently stopped quoting the passage at verse. 31. When we continue reading the passage, we find that this very same man, and his household, were immediately Baptized (and there is no mention of the manner of baptism, but submersion in this context appears to be VERY unlikely in the minds of most scholars today).
Acts 16:29. And he called for lights and rushed in, and trembling with fear he fell down before Paul and Silas,
30. and after he brought them out, he said, "Sirs, what must I do to be saved?"
The Jailer Converted
31. They said, "Believe in the Lord Jesus, and you will be saved, you and your household."
32. And they spoke the word of the Lord to him together with all who were in his house.
33. And he took them that
very hour of the night and washed their wounds, and immediately he was baptized, he and all his
household.
34. And he brought them into his house and set food before them, and rejoiced greatly, having believed in God with his whole household.
Indeed, in the New Testament Church and in the Church for the next 300 years, belief in Christ as Lord and Savior, water baptism, and being baptized into the body of Christ are very closely connected and the three are often seen as being inseparable. Indeed, in the New Testament itself we read,
Mark16:16. "He who has believed and has been baptized shall be saved; but he who has disbelieved shall be condemned.”
Act 2:37. Now when they heard this, they were pierced to the heart, and said to Peter and the rest of the apostles, "Brethren, what shall we do?"
38. Peter said to them, "Repent, and each of you be baptized in the name of Jesus Christ for the forgiveness of your sins; and you will receive the gift of the Holy Spirit.
39. "For the promise is for you and your children and for all who are far off, as many as the Lord our God will call to Himself."
Rom. 6:1. What shall we say then? Are we to continue in sin so that grace may increase?
2. May it never be! How shall we who died to sin still live in it?
3. Or do you not know that all of us who have been baptized into Christ Jesus have been baptized into His death?
4. Therefore we have been buried with Him through baptism into death, so that as Christ was raised from the dead through the glory of the Father, so we too might walk in newness of life.
5. For if we have become united with
Him in the likeness of His death, certainly we shall also be
in the likeness of His resurrection,
6. knowing this, that our old self was crucified with
Him, in order that our body of sin might be done away with, so that we would no longer be slaves to sin;
7. for he who has died is freed from sin.
8. Now if we have died with Christ, we believe that we shall also live with Him,
9. knowing that Christ, having been raised from the dead, is never to die again; death no longer is master over Him.
10. For the death that He died, He died to sin once for all; but the life that He lives, He lives to God.
11. Even so consider yourselves to be dead to sin, but alive to God in Christ Jesus.
1 Pet. 3:18. For Christ also died for sins once for all, the just for the unjust, so that He might bring us to God, having been put to death in the flesh, but made alive in the spirit;
19. in which also He went and made proclamation to the spirits now in prison,
20. who once were disobedient, when the patience of God kept waiting in the days of Noah, during the construction of the ark, in which a few, that is, eight persons, were brought safely through the water.
21. Corresponding to that, baptism now saves you--not the removal of dirt from the flesh, but an appeal to God for a good conscience--through the resurrection of Jesus Christ,
22. who is at the right hand of God, having gone into heaven, after angels and authorities and powers had been subjected to Him.