1. The problem is to calculate the value of $\eta$ given by the formula: $$\eta = \frac{314 \cdot (1.96)^2 \cdot 0.613 \cdot (1 - 0.613)}{(0.1)^2 (314 - 1) + (1.96)^2 \cdot 0.613 \cdot (1 - 0.613)}$$ 2. This formula involves multiplication, powers, subtraction, and division. We will calculate the numerator and denominator separately before dividing. 3. Calculate the numerator: - Compute $1 - 0.613 = 0.387$ - Compute $(1.96)^2 = 3.8416$ - Multiply all terms: $314 \times 3.8416 \times 0.613 \times 0.387$ Calculate step-by-step: $$314 \times 3.8416 = 1206.5024$$ $$1206.5024 \times 0.613 = 739.586972$$ $$739.586972 \times 0.387 = 286.1539$$ So, numerator $\approx 286.1539$ 4. Calculate the denominator: - Compute $(0.1)^2 = 0.01$ - Compute $314 - 1 = 313$ - Multiply: $0.01 \times 313 = 3.13$ - Compute $(1.96)^2 = 3.8416$ (already calculated) - Compute $0.613 \times 0.387 = 0.237031$ - Multiply: $3.8416 \times 0.237031 = 0.9101$ Sum the two parts: $$3.13 + 0.9101 = 4.0401$$ 5. Finally, divide numerator by denominator: $$\eta = \frac{286.1539}{4.0401} \approx 70.81$$ Therefore, the value of $\eta$ is approximately $70.81$.