Question

Don’t drink the water!The movie A Civil Action ($1998$) tells the story of a

major legal battle that took place in the small town of Woburn, Massachusetts. A town well that supplied water to east Woburn residents was contaminated by industrial chemicals. During the period that residents drank water from this well, $16$of $414$babies born had birth defects. On the west side of Woburn, $3$of $228$babies born during the same time period had birth defects. Let $p_1$be

the true proportion of all babies born with birth defects in west Woburn and $p_2$be the true proportion of all babies born with birth defects in east Woburn. Check if the conditions for calculating a confidence interval for$p_1-p_2$are met.

Short answer

It is not fit to find confidence interval for$p_1-p_2$

Step-by-step solution

Given Information

It is given that $n_1=414$

$x_1=16$

$n_2=228$

$x_2=3$

Explanation

Testing three conditions:

1. Random: As it is arbitrarily assigned, it is not met.

2. Independent: Due to used all values in population and not used sample, it is not satisfied.

3. Normal: There are only three success which is less than ten.

All conditions are not satisfied, it is not fit to find confidence interval$p_1-p_2$