A medical research firm obtained a nationwide registry of $N=4800$ adults diagnosed with Type II diabetes and needs a sample of $n=40$. The registry contains counts by age strata: $18\text{–}39$ has $N_1=1200$, $40\text{–}59$ has $N_2=2000$, and $60+$ has $N_3=1600$. Which sampling design and selection procedure is most appropriate to obtain a representative sample of $n=40$?

Use convenience sampling at three large clinics until each age group has approximately $\frac{1}{3}n$ respondents

Use a single simple random sample of $n=40$ from the entire registry without stratification.

Use cluster sampling by randomly selecting $40$ doctors and surveying all their diabetic patients.

Use proportional stratified sampling with $n_h=\frac{N_h}{N}\times n$ and then perform a simple random sample without replacement within each stratum, giving $n_1=10,n_2=17,n_3=13$.