A manufacturer of small appliances purchases plastic handles for coffeepots from an outside vendor. If a handle is cracked, it is considered defective and can't be used. A large shipment of plastic handles is received. How many handles from the shipment should be inspected in order to estimate p, the proportion of defective handles in the shipment, with a margin of error of 0.13 or less? (Assume a confidence level of 95%).

Question

A manufacturer of small appliances purchases plastic handles for coffeepots from an outside vendor. If a handle is cracked, it is considered defective and can't be used. A large shipment of plastic handles is received. How many handles from the shipment should be inspected in order to estimate p, the proportion of defective handles in the shipment, with a margin of error of 0.13 or less? (Assume a confidence level of 95%). ​

Quizplus · Accepted Answer

To estimate the proportion with a margin of error of 0.13 at a 95% confidence level, the sample size can be calculated using the formula for sample size in proportion estimation: n = (Z^2 * p * (1-p)) / E^2. Assuming p = 0.5 for maximum variability, Z = 1.96 for 95% confidence, and E = 0.13, the calculation gives approximately 57 handles.

A Manufacturer of Small Appliances Purchases Plastic Handles for Coffeepots