According to the geological record, during which geological time period were the sands and clays underlying Long Island and Staten Island deposited?

The correct answer is - Cretaceous period.

Explanation:

The Magothy Formation occurred during the cretaceous period. The Magothy formation is the formation of the consolidated sand and layers of clays deposited beneath  Quaternary glacial cover throughout most of Long Island, and the south shore of Staten Island.

This formation is composed of gravel of clay and coarse sands. The thickness ranges between 10 and 200 feet. It is formed above the Raritan Formation which is upper clay and below slit deposits formation.

you didn't give any options but heres what i can tell you: an inference is likely to change based on additional observations. the latter is something that you have seen or sensed using your sensory organs while the former is like a conclusion out from what you have observed.