Step 1: Understanding the Concept:
The basicity of amines is dependent on the availability of the lone pair on the nitrogen atom and the stability of the substituted ammonium cation formed after accepting a proton in water.
Step 2: Key Formula or Approach:
Evaluate the factors influencing amine basicity in an aqueous solution (Inductive effect, Solvation, Steric hindrance) and identify the unrelated electronic factor.
Step 3: Detailed Explanation:
In the aqueous phase, three main factors compete to determine the order of basicity of alkylamines:
1. Inductive effect ($+I$): Alkyl groups are electron-donating, which pushes electron density toward nitrogen, making the lone pair more available and increasing basicity.
2. Solvation effect: Smaller substituted ammonium cations (from primary amines) are more stabilized by hydrogen bonding with water molecules than larger ones (from tertiary amines).
3. Steric hindrance: Large alkyl groups physically hinder the approach of protons or the hydration of the resulting cation, decreasing basicity.
Hyperconjugation involves the delocalization of $\sigma$ electrons of $C-H$ bonds into an adjacent empty p-orbital or $\pi$ system. It does not play a role in the availability of the non-bonding lone pair on the saturated $sp^3$ nitrogen of alkylamines.
Step 4: Final Answer:
Hyperconjugation effect does not decide the basic strength of alkylamines.