Question

A truck loaded with 8000 electronic circuit boards has just pulled into a firm’s receiving dock. The supplier claims that no more than 3% of the boards fall outside the most rigid level of industry performance specifications. In a simple random sample of 300 boards from this shipment, 12 fall outside these specifications. Calculate the upper confidence limit of the 95% confidence interval for the percentage of all boards in this shipment that fall outside the specification.

Answer 1

Solution :

Given that,

n = 300

x = 12

Point estimate = sample proportion = = x / n = 12 / 300 = 0.04

1 - = 1 - 0.04 = 0.96

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

Z = Z _0.05 = 1.645

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

= 1.645 * (((0.04 * 0.96) / 300)

= 0.019

The upper confidence limit of the 95% confidence interval for population proportion p is ,

+ E = 0.04 - 0.019 = 0.021

upper confidence limit = 0.021