To analyze the confidence interval [tex]\(-0.000482 < p_1 - p_2 < -0.000329\)[/tex], we can make several important observations about the claim regarding the rate of polio in children given the vaccine compared to those given a placebo.
1. The confidence interval does not contain 0. This suggests that there is a statistically significant difference between the two proportions being compared.
2. Given that the entire confidence interval is negative, it appears there is a significant difference between the two proportions, with [tex]\(p_1 < p_2\)[/tex].
3. The first proportion (children given the vaccine) is less than the second proportion (children given the placebo). This suggests that the rate of polio is lower for children given the vaccine compared to those given a placebo.
4. There is sufficient evidence to support the claim that the rate of polio is less for children given the vaccine than it is for children given a placebo.
Therefore, the completed analysis should read as follows:
- Because the confidence interval does not contain [tex]\(\boxed{0}\)[/tex].
- [tex]\(\boxed{There}\)[/tex] appears to be a significant difference between the two proportions. Because the confidence interval.
- [tex]\(\boxed{does~not~contain~}\)[/tex] the pooled sample proportion, it appears that the first proportion is [tex]\(\boxed{less~than}\)[/tex] the second proportion. There is [tex]\(\boxed{sufficient}\)[/tex] evidence to support the claim that the rate of polio is less for children given the vaccine than it is for children given a placebo.
