Concept: Basic strength is inversely proportional to the acidity of the conjugate acid. A weaker conjugate acid corresponds to a stronger conjugate base.
Step 1: {Identify the conjugate acids of the given bases.}
• (A) NH$_2^-$ $\rightarrow$ NH$_3$ (Ammonia)
• (B) OH$^-$ $\rightarrow$ H$_2$O (Water)
• (C) CH$\equiv$C$^-$ $\rightarrow$ CH$\equiv$CH (Acetylene)
• (D) CH$_3$CH$_2^-$ $\rightarrow$ CH$_3$CH$_3$ (Ethane)
• (E) OEt$^-$ $\rightarrow$ EtOH (Ethanol)
Step 2: {Compare the acidity of the conjugate acids.}
Ethane (alkane) is the least acidic among these compounds because carbon is less electronegative than Nitrogen or Oxygen and lacks s-character (sp$^3$ hybridized).
$$\text{Acidity order: } \text{H}_2\text{O} > \text{EtOH} > \text{CH}\equiv\text{CH} > \text{NH}_3 > \text{CH}_3\text{CH}_3$$
Step 3: {Determine the strongest base.}
Since Ethane is the weakest acid, its conjugate base, the ethyl anion (CH$_3$CH$_2^-$), is the strongest base.