Answer to Question #198757 in Statistics and Probability for jeff

Question

a leading medical journal claims that 39% of young adults play organized sports. a physician wants to conduct a survey to verify this with her young adult patients and wants to do so with a margin error of (ME) of +-5%. what minimum sample size, rounded to the nearest whole person, does the physician need to use?

Answer 1

For 0.05 level of significance:

$ME=1.96\sqrt{\frac{p(1-p)}{n}}$

$0.05=1.96\sqrt{\frac{0.39(1-0.39)}{n}}$

$n=(\frac{1.96}{0.05})^2*0.39(1-0.39)=366.$