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 must be discarded. A large shipment of plastic handles is received. The proportion of defective handles p is of interest. How many handles from the shipment should be inspected to estimate p to within 0.09 with 95% confidence?

Answer 1

Answer: 119

Step-by-step explanation:

Since the prior estimate of population proportion of defective handles  (p) is unknown , so we take p= 0.5

Given : Margin of error : E=0.09

Critical value for 95% confidence interval : $z_{\alpha/2}=1.96$

Required sample size :-

$n=0.5(1-0.5)(\dfrac{z_{\alpha/2}}{E})^2\\\\=0.25(\dfrac{1.96}{0.09})^2\\\\=118.567901235\approx119$

Hence, the minimum sample size required = 119

i.e. 119 handles from the shipment should be inspected.