When the sample size is small, the large sample approximation for proportions is

Question

When the sample size is small, the large sample approximation for proportions is inaccurate. In this case, a simple modification called the plus four estimate is used for the sample proportion in the calculation of confidence intervals. Consider the following example: A researcher planning an experiment collects a sample of 10 female subjects who were measured on their equol production. It was found that 4 among them were equol producers, and the rest were non producers. The researcher would like to estimate the proportion of equol producers in the population. In forming a confidence interval, what will be the plus four estimate of the proportion of equol producers?

Explanation / Answer

using the formula

p = (X+2)/(n+4) where X is number of sucess,n is number of size, p is the plus four estimate, n is size

p= (4+2)/(10+4) =6/14

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