Confidence interval estimate

[maresa707]

In randomized, double-blind clinical trails of a new vaccine, subjects were randomly divided into two groups. Subjects in group 1 receieved the new vaccine while subjects in group 2 received a control vaccine. After the first dose, 114 of 710 subjects in the experimental group 1 experienced vomiting as a side effect. After the first dose 71 of 631 of the subjects in the control group 2 experienced vomiting as a side effect. Construst a 95% confidence interval for the difference between the two population proportions, p1-p2 construst a 95% confidence interval estimate.
< p1-p2< Round to three
Please help me solve this

 

[galactus]

I use Excel for this. Most calculators will do these (TI-83 will). Do not do these by hand unless you're made to. The formulas are cumbersome.

I ran it through Excel and got \(\displaystyle .0115\leq p_{1}-p_{2}\leq .0846\).

This is based on a two-tail, of course.

This says that we can be 95% confident that the difference in the proportions will be between those values.

The difference in the given proportions is .048, so it falls in the CI.