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

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

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

$$CI=(0.207960, 0.592040)$$