12 The percentage of patients overdue for a vaccination is often of interest for

Question

12 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

Explanation / Answer

a. Here p=0.5, E=0.10 and z=1.96

As we know Margin of Error=E=z*sqrt(pq/n)

n=(z/E)^2*pq

n=(1.96/0.10)^2*0.5*0.5=96.04=97

b. Here p=27/120=0.225

Hence n=(1.96/0.10)^2*0.225*0.775=66.9879=67

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