A quality manager in a small manufacturing company wants to estimate the proportion of items produced by a very specialized process that fail to meet a customer's specification.Because it is very expensive to determine if an item produced by the process meets the specification,only a very small number of items can be tested.A random sample of 15 items was selected,and in the sample three of them failed.What is the standard error of the plus four estimate of the true proportion p?
A)0.010
B)0.103
C)0.101
D)0.116
E)0.013

Question

Quizplus · Accepted Answer

The plus four estimate of the true proportion p is calculated as:
(p̂+2)/(n+4), where n is the sample size and p̂ is the sample proportion of failures.
In this case, n=15 and p̂=3/15=0.2
So the plus four estimate is:
(p̂+2)/(n+4) = (0.2+2)/(15+4) = 0.1429
To calculate the standard error of this estimate, we use the formula:
√[p̂(1-p̂)/(n+4)] = √[0.2(0.8)/(15+4)] = 0.1007
Therefore, the answer is choice C) 0.101.

A Quality Manager in a Small Manufacturing Company Wants to Estimate