Statement-1: The atomic radii of the elements of the oxygen family are smaller than the atomic radii of the corresponding elements of the nitrogen family.

Statement-2: The members of the oxygen family are more electronegative and thus have lower values of nuclear charge than those of the nitrogen family

The atomic radii of the oxygen-family elements are smaller than those of the comparable nitrogen-family elements.
From group 15 to group 16, the effective nuclear charge rises. In group 16 elements compared to group 15 elements, this causes a stronger nuclear pull on the electrons.
So, while the statement-1 is true, the statement-2 is false.