Answer to Question #86252 in Statistics and Probability for Anand

Question

Out of 25 newborn babies of obese women, 10 weigh less than 2.5 kg. Find a 95% confidence interval for the probability that the weight of a newborn baby of an obese woman is less than 2.5 kg.

Answer 1

Sample proportion

$\widehat{p}=10/25=0.4$

A 95% confidence interval for the probability that the weight of a newborn baby of an obese woman is less than 2.5 kg is

$CI=( \widehat{p}-z^*\sqrt{\widehat{p}*(1-\widehat{p})/n}, \widehat{p}+z^*\sqrt{\widehat{p}*(1-\widehat{p})/n})$ $z^*=1.96$

$CI=( 0.4-1.96*\sqrt{0.4*(1-0.4)/25}, 0.4+1.96*\sqrt{0.4*(1-0.4)/25})$

$CI=(0.207960, 0.592040)$