| Estimación de la media | Estimación de una Proporción | Estimacion de un Total |
|---|---|---|
| \(\overline{y}_{st}=\frac{1}{N}\sum{N_i\overline{y}_i}\) | \(N\overline{y}_{st}=\sum{N_i\overline{y}_i}\) | \(\overline{p}_{st}=\frac{1}{N}\sum{N_i\overline{p}_i}\) |
El Error es dos veces la raiz cuadrada de estimación la estimación de la varianza de la distribución muestral de la media.
| La media | Total: | Proporción: |
|---|---|---|
| \(\widehat{V}(\overline{y}_{st})=\frac{1}{N^2}\sum_{i=1}^{L}(N_i^2\frac{N_i-n_i}{Ni})(\frac{s_i^2}{n_i})\) | \(\widehat{V}(N\overline{y}_{st})=N^2\widehat{V}(\overline{y}_{st})=\sum_{i=1}^{L}(N_i^2\frac{N_i-n_i}{Ni})(\frac{s_i^2}{n_i})\) | \(\widehat{V}(\overline{y}_{st})=\frac{1}{N^2}\sum_{i=1}^{L}(N_i^2\frac{N_i-n_i}{Ni})(\frac{\widehat{p}_i\widehat{q}_i}{n_i})\) |
Estimar media Medias.
| con proporciones | con costos | con Neyman | proporcional |
|---|---|---|---|
| \(n=\frac{\left( \sum_{k=1}^{L}\frac{N_k^2\sigma_k^2}{a_i} \right)}{N^2B^2/4+\sum_{i=1}^{L}N_i\sigma_i^2}\) | \(n=\frac{\left( \sum_{k=1}^{L}\frac{N_k\sigma_k}{\sqrt{c_k}} \right)\left( \sum_{i=1}^{L}N_i\sigma_i{\sqrt{c_k}} \right)}{N^2B^2/4+\sum_{i=1}^{L}N_i\sigma_i^2}\) | \(n=\frac{\left( \sum_{k=1}^{L}{N_k\sigma_k} \right)^2}{N^2\frac{B^2}{4}+\sum_{i=1}^{L}N_i\sigma_i^2}\) | \(n=\frac{\left( \sum_{k=1}^{L}{N_k\sigma_k^2} \right)}{N\frac{B^2}{4}+1/N\sum_{i=1}^{L}N_i\sigma_i^2}\) |
Total
\(n=\frac{\left( \sum_{k=1}^{L}\frac{N_k^2\sigma_k^2}{a_i} \right)}{B^2/4+\sum_{i=1}^{L}N_i\sigma_i^2}\) \(n=\frac{\left( \sum_{k=1}^{L}\frac{N_k\sigma_k}{\sqrt{c_k}} \right)\left( \sum_{i=1}^{L}N_i\sigma_i{\sqrt{c_k}} \right)}{N^2\frac{B^2}{4N^2}+\sum_{i=1}^{L}N_i\sigma_i^2}\) \(n=\frac{\left( \sum_{k=1}^{L}{N_k\sigma_k} \right)^2}{N^2\frac{B^2}{4N^2}+\sum_{i=1}^{L}N_i\sigma_i^2}\)
Proporción \(n=\frac{\left( \sum_{k=1}^{L}N_i^2p_iqi/a_i \right)}{N^2B^2/4+\sum_{i=1}^{L}N_ip_iq_i}\)
para Media:
\(n_i=n\left( \frac{N_i\sigma_i/\sqrt{c_i}}{\sum_{k=1}^{L}N_k\sigma_k/\sqrt{c_k}} \right)\)