To reduce the maximum number of collisions in the hash table described in the above question, someone proposed the use of a larger array of 14 elements and of course modifying the hash function to: h(k)=k mod 14. The idea was to reduce the load factor and hence the number of collisions.

Does this proposal hold any validity to it? If yes, indicate why such modifications would actually reduce the number of collisions. If no, indicate clearly the reasons you believe/think that such proposal is senseless.