Question

We want to estimate the probability of failure p in a production process by observing n objects produced, chosen independently. It is known that p is between 0.1 and 0.3, due to the previous information available on the process. You want to find the sample size so that the probability of the proportion of defective objects in the sample differs from the true p-value by less than 0.01 is less than 0.95.

Answer 1

We are given the margin of error here as: p = 0.01

As the confidence level given here is the probability value of 0.95

From standard normal tables, we have here:
P( -1.96 < Z < 1.96) = 0.95

Also to get a conservative value of n, we use a greater value of prior proportion value of p here as 0.3 which is given as p = 0.3

The margin of error here is computed as:

Therefore 8068 is the required sample size here.