Step 1: Analyze Each Statement  
Statement 1: Basic Nature of Hydroxides  
- The basicity of hydroxides increases down the group due to decreasing ionization energy and increasing lattice solubility.  
- The correct order:  
  \[
  {Mg(OH)}_2<{Ca(OH)}_2<{Sr(OH)}_2<{Ba(OH)}_2
  \]
- This statement is correct.  
Statement 2: Thermal Stability of Carbonates  
- Incorrect because the thermal stability of carbonates increases down the group.  
- BeCO₃ is the least thermally stable, while BaCO₃ is the most stable.  
- Correct order:  
  \[
  {BeCO}_3<{MgCO}_3<{CaCO}_3<{SrCO}_3<{BaCO}_3
  \]
- This statement is incorrect, making it the correct answer to the question.  
Statement 3: Solubility of Sulphates  
- Solubility decreases down the group as hydration energy decreases.  
- Correct order:  
  \[
  {BeSO}_4>{MgSO}_4>{CaSO}_4>{SrSO}_4>{BaSO}_4
  \]
- This statement is correct.  
Statement 4: Nitrate Decomposition  
- All alkaline earth metal nitrates decompose on heating to form metal oxides, NO₂, and O₂.  
- Example reaction:  
  \[
  {Ca(NO}_3)_2 \rightarrow {CaO} + 2{NO}_2 + \frac{1}{2} O_2
  \]
- This statement is correct.  
Final Answer: Statement 2 is incorrect.