Question

A company receives shipments of a component used in the manufacture of a component for a high-end acoustic speaker system. When the components arrive, the company selects a random sample from the shipment and subjects the selected components to a rigorous set of tests to determine if the components in the shipments conform to their specifications. From a recent large shipment, a random sample of 250 of the components was tested, and 24 units failed one or more of the tests. At the 98% level of confidence, what is the margin of error in the point estimate of the proportion of components in the shipment that fail to meet the company's specifications?

Answer 1

Solution :

Given that,

n = 250

x = 24

Point estimate = sample proportion = = x / n = 24 / 250 = 0.096

1 - = 1 - 0.096 = 0.904

At 98% confidence level

= 1 - 98%

=1 - 0.98 =0.02

/2 = 0.01

Z/2 = Z0.01 = 2.326

Margin of error = E = Z / 2 * (( * (1 - )) / n)

Margin of error = E  = 2.326 (((0.096 * 0.904) / 250 )

Margin of error = E = 0.043