The percentage of patients overdue for a vaccination is often of interest for a medical clinic Some clinics examine every record to determine that percentage; in a large practice, though, taking a census of the records can be time-consuming. Cullen (1994) took a sample of the 580 children served by an Auckland family practice to estimate the proportion of interest.

a What sample size in an SRS (without replacement) would be necessary to estimate the proportion with 95% confidence and margin of error 0.10?

b Cullen actually took an SRS with replacement of size 120, of whom 27 were not overdue for vaccination. Give a 95% CI for the proportion of children not overdue for vaccination.

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