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 lower confidence limit of the 95% confidence interval for the percentage of all boards in this shipment that fall outside the specification.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 lower confidence limit of the 95% confidence interval for the percentage of all boards in this shipment that fall outside the specification.

Answer 1

Ans. We have given a sample of 300 boards from the shipment, out of which 12 fall outside the industry performance specification.But the supplier claims it that no more than 3% of boards fall outside the industry performance specification.

Sample proportion,

This sample proportion is use to estimate, 95% confidence interval for the parameter p, which is the population proportion, that is fall outside the performance specification.

The formula for Confidence interval is:

For 95% confidence,

Lower limit of the confidence interval :

Or 1.78%

So the percentage of proportion of all boards that fall outside the performance specification is greater than 1.78%.