A fire occurs in a massive warehouse used to store apples prior to shipment.The apples are held in individual crates.The insurance company wishes to estimate the proportion of crates that were damaged by smoke from the fire.How many crates should the insurance adjustor analyze if she wishes to construct a 98% confidence interval with a bound on the error of estimation of 0.02?
A) 3383
B) 34
C) 2401
D) 4147

Question

Quizplus · Accepted Answer

To construct a 98% confidence interval with a bound on the error of estimation (E) of 0.02, we use the formula for sample size in estimating proportions: $n = \frac{Z^2 \cdot p \cdot (1-p)}{E^2}$. Assuming we don't know the true proportion (p), we use the most conservative estimate, which is 0.5. For a 98% confidence level, the Z-value is approximately 2.33 (from Z-tables). Plugging these values into the formula gives: $n = \frac{(2.33)^2 \cdot 0.5 \cdot (1-0.5)}{(0.02)^2}$, which calculates to approximately 3383.

A Fire Occurs in a Massive Warehouse Used to Store