Answer
Since the traditional method relies on the multiplication of probabilities, it will yield 0 as the result. Hence, we use Agresti and Coull’s method in this case.
Lower Bound = 0.04, Upper Bound = 0.326
Work Step by Step
Here x = 0, n = 10, α = 0.05, $z_{0.025} = 1.96$
$\tilde p = \frac{0 + 2}{10+4} = 0.143$
Lower Bound = $0.143 - 1.96 . \sqrt \frac{0.143 (1-0.143)}{10+4} = 0.04$
Upper Bound = $0.143 + 1.96 . \sqrt \frac{0.143 (1-0.143)}{10+4} = 0.326$
