Question

"Antibiotic Resistance Puzzle" reports that children in a certain city "are resistant to common antibiotics at a rate that is double the national average [...] To look at local resistance rates, the Children's Hospital researchers tested 708 cultures of Group A strep that were obtained from pediatric patients between September 2001 and May 2002. Overall, 68 (or 9.6%) of the strep samples were resistant to macrolides. [...] Studies conducted elsewhere indicate a national macrolide resistance rate of about 5%."

(1) To justify use of a normal approximation, the observed numbers in and out of the category of interest must be at least 10. What are those two numbers in this case?

(2) Report an approximate 95% confidence interval for the proportion of all Group A strep cultures from the area that would be resistant to macrolides. (Round your answers to two decimal places.)

Answer 1

Given : Sample size=n=708

Sample proportion=p=0.096

(1) Here , np=708*0.096=68>10 and nq=708*(1-0.096)=640.0320>10

Therefore , use the normal approximation

(2) The 95%  confidence interval for the proportion of all Group A strep cultures from the area that would be resistant to macrolides is ,

; ; From standard normal probability table