In some situations involving proportions, you are interested in the ratio = p 1 / p

In some situations involving proportions, you are interested in the ratio θ = p₁ / p₂ rather than the difference p₁ – p₂. Let θ = p₁ / p₂. It can be shown that ln(θ) has an approximate normal distribution with the mean (n / θ) and variance (n₁ – x₁) / (n₁ x₁) + (n₂ – x₂) / (n₂ x₂)^1/2.

(a) Use the preceding information to derive a large-sample confidence interval for ln θ.

(b) Show how to find a large-sample CI for θ.

(c) Use the data from the St. John’s Wort study in Example 10-16, and find a 95% CI on θ = p₁ / p₂. Provide a practical interpretation for this CI.