A survey of food allergies in a simple random sample of 184 young children found that 13 had some kind of food allergy. Why should we use the plus four method to compute a 95% confidence interval for the population proportion of young children who have a food allergy?

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The plus four method is used to compute a 95% confidence interval when the counts of successes (13 children with food allergies) and failures (184 - 13 = 171 children without food allergies) in the sample are too small for the large-sample method to be appropriate. This method adds two successes and two failures to the sample to adjust for the small sample size, ensuring a more accurate estimation of the confidence interval.

A Survey of Food Allergies in a Simple Random Sample