Answer :
The sample required to estimate the true proportion of homeowners who have vegetable gardens is 472.
The formula for calculating a confidence interval proportion is given by
E = Z×√(p×q÷n).
where
E = maximum allowance of error between the true proportion and the sampling proportion.
Z = the confidence interval in standard error units.
p = The estimated proportion of success
q = (1-p), or the estimated proportion of failures.
n = no of items in a sample.
Solving the equation for n, we get
n = (Z²×p×q)÷(E²)
Substituting the values based on the equation based on the sampling design, we get
n = [1.7507² × 0.44 × 0.56]÷(0.04)²
Solving the equation, the value of n is obtained as
n = 472, when rounded up.
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