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.Based on the sample results,the plus four estimate of the true proportion of items that failed to meet the customer's specifications is _______.
A) = 0.200
B) = 0.158
C) = 0.333
D) = 0.263
E)Not within ± 0.02 of any of the above

Question

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.Based on the sample results,the plus four estimate of the true proportion of items that failed to meet the customer's specifications is _______.
A) = 0.200 
B) = 0.158 
C) = 0.333 
D) = 0.263 
E)Not within ± 0.02 of any of the above

Quizplus · Accepted Answer

The plus-four method is used when the sample size is small and the true population proportion is unknown. It's a modification of the maximum likelihood method that adds four imaginary observations, two successes, and two failures, to the sample. In this case, the sample size is small (n=15), and the true population proportion is unknown, so we can use plus-four estimate.

The formula for the plus-four estimate of the proportion is:

p = (x + 2) / (n + 4)

where:
p = plus-four estimate of the proportion
x = number of items that failed in the sample
n = sample size

Substituting the given values, we get:

p = (3 + 2) / (15 + 4) = 0.263

Therefore, the plus-four estimate of the true proportion of items that failed to meet the customer's specifications is 0.263 or approximately 0.26. The closest choice is D, so the answer is D.

A Quality Manager in a Small Manufacturing Company Wants to Estimate