Some try to use the instances of household baptism in the New Testament as support for the baptism of infants. That this was not the case is shown by the fact that often when people and their household are baptised it is stated that they believed and were baptised. This demonstrates that only those of sufficient age to be capable of believing were baptised.

Cornelius, his relatives and close friends: the Holy Spirit fell upon them, the gift of the Holy Spirit had been poured out upon the Gentiles, they were speaking with tongues and exalting God, they had received the Holy Spirit just as Peter and the brethren from Joppa had (Acts 10:23, 24, 44-48).

Lydia and her household: no statement concerning the household. (Acts 16:14-15)

The Phillippian jailor: Believe^singular in the Lord Jesus, and you^singular shall be saved, you and your household (Acts 16:31). ... having believed in God with his whole household (Acts 16:34). ie v 31 emphasizes both that the jailor himself must believe and be saved, but also that the same condition applies to his household. v 34 makes it clear that the whole household believed.

Crispus: believed in the Lord with all his household, and many of the Corinthians when they heard were believing and being baptised (Acts 18:8).