Question: Claim: p ≥ 0.44; α = 0.04. Sample statistics: p̂ = 0.40, n = 150 … Let q = 1 - p and let q̂ = 1 -…

Claim: p ≥ 0.44; α = 0.04. Sample statistics: p̂ = 0.40, n = 150 … Let q = 1 - p and let q̂ = 1 - p̂. A normal sampling distribution can be used here, since ▼ ▼ 5 and ▼ ▼ 5.

Solution

To determine if a normal sampling distribution can be used, we need to check if both \( np \) and \( nq \) are greater than or equal to 5. Given: - \( p = 0.44 \) - \( \hat{p} = 0.40 \) - \( n = 150 \) 1. Calculate \( q = 1 - p = 1 - 0.44 = 0.56 \). 2. Calculate \( np \): \[ np = 150 \times 0.44 = 66 \] 3. Calculate \( nq \): \[ nq = 150 \times 0.56 = 84 \] Since both \( np = 66 \) and \( nq = 84 \) are greater than 5, a normal sampling distribution can be used.