How likely are patients who file complaints with a health maintenance organizati

Question

How likely are patients who file complaints with a health maintenance organization (HMO) to leave the HMO? In one year, 676 of the more than 400,000 members of a large New England HMO filed complaints. Fifty-two of the complainers left the HMO voluntarily. (That is, they were not forced to leave by a move or a job change.) Consider this year's complainers as an SRS of all patients who will complain in the future. Give a 90% confidence interval for the proportion of complainers who voluntarily leave the HMO. (Round your answers to three decimal places.)

Explanation / Answer

here estimated proportion phat=x/n=52/676=0.0769

std error=(phat*(1-phat)/n)1/2 =0.0102

for 90% CI ; critical value of z =1.6449

90% confidence interval for the proportion of complainers who voluntarily leave the HMO

=sample proportion -/+ z*Std error =0.060 ; 0.094

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