Question

A pharmaceutical company proposed a vaccine that would combat paralytic polio. two independent random samples were collected from the population. one random sample of 229 was given the placebo, and among them 115 contracted paralytic polio. the other random sample of 245 was given the vaccine, and among them 61 people ended up contracting paralytic polio. let the true proportion of cases of paralytic polio given placebo be p1 and the true proportion of cases of paralytic polio given vaccine be p2 . calculate the upper bound of a 95% confidence interval for p1−p2 . round your answer to three decimal places.

Answer 1

The upper bound of the 95% confidence interval for p1 - p2 is 0.349.

Step-by-step explanation:

To calculate the upper bound of a 95% confidence interval for the difference in proportions, we need to calculate the standard error and the margin of error.

1. Calculate the sample proportions for each group: p1 = number of cases of paralytic polio in placebo group / size of placebo group and p2 = number of cases of paralytic polio in vaccine group / size of vaccine group.
2. Calculate the standard error: SE = sqrt((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)), where n1 is the size of the placebo group and n2 is the size of the vaccine group.
3. Calculate the margin of error: ME = 1.96 * SE
4. Calculate the upper bound of the confidence interval: upper bound = (p1 - p2) + ME.

Plugging in the given values, we get:

• p1 = 115 / 229 = 0.502
• p2 = 61 / 245 = 0.249
• SE = sqrt((0.502 * (1 - 0.502) / 229) + (0.249 * (1 - 0.249) / 245)) = 0.049
• ME = 1.96 * 0.049 = 0.096
• upper bound = (0.502 - 0.249) + 0.096 = 0.349

Therefore, the upper bound of the 95% confidence interval for p1 - p2 is 0.349.