Answer:
The recommended sample size is 1,698
Step-by-step explanation:
The given standard deviation in milk consumption per capita across the U.S., σ = 4 ounces
The required confidence level = 95%
The margin of error, e = ± 0.5
When the precision is doubled, we have the new margin of error = ±0.5/2 = ±0.25
The standard score at 99% confidence level, z = 2.576
The sample size formula is given as follows;
![S = \dfrac{Z^2 \times P \times Q}{E^2}](https://tex.z-dn.net/?f=S%20%3D%20%5Cdfrac%7BZ%5E2%20%5Ctimes%20P%20%5Ctimes%20Q%7D%7BE%5E2%7D)
Where;
P × Q = The variance = σ²
∴ P × Q = 4² = 16
The sample size becomes;
S = 2.576² × 16/(0.25²) = 1,698.758656
We round down to get the recommended sample size, S = 1,698