1. **State the problem:** We have a population of 15 units with values $X_i$ and $Y_i$ and random numbers $\epsilon_i$. We need to select a sample of size 7 using Simple Random Sampling (SRS) and estimate the total $E$ and mean $\mu$ of the sample. 2. **Formula and rules:** - Total estimate for SRS: $$\hat{t} = N \times \bar{y}_s$$ where $N=15$ is population size, $\bar{y}_s$ is sample mean. - Mean estimate: $$\hat{\mu} = \bar{y}_s$$ - Sample mean: $$\bar{y}_s = \frac{1}{n} \sum_{i=1}^n y_i$$ where $n=7$ is sample size. 3. **Select sample using SRS:** Use the random numbers $\epsilon_i$ to select 7 units with smallest $\epsilon_i$ values. Sorted $\epsilon_i$ with units: 0.038(5), 0.112(11), 0.117(3), 0.150(4), 0.190(13), 0.274(14), 0.387(2) Selected units: 5, 11, 3, 4, 13, 14, 2 4. **Extract $Y_i$ values for selected units:** Unit 5: 32 Unit 11: 29 Unit 3: 20 Unit 4: 30 Unit 13: 12 Unit 14: 30 Unit 2: 31 5. **Calculate sample mean:** $$\bar{y}_s = \frac{32 + 29 + 20 + 30 + 12 + 30 + 31}{7} = \frac{184}{7} \approx 26.29$$ 6. **Estimate total:** $$\hat{t} = 15 \times 26.29 = 394.29$$ 7. **Estimate mean:** $$\hat{\mu} = 26.29$$ **Final answers:** - Estimated total $E = 394.29$ - Estimated mean $\mu = 26.29$