Question

1. Researchers comparing the effectiveness of two pain medications randomly selected a group of patients who had been complaining of a certain kind of joint pain. They randomly divided these people into two groups, and then administrated the pain killer. Of the 112 people in the group who received medication A, 84 said this pain reliever was effective. Of the 108 people in the other group, 66 reported that pain reliever B was effective.
   1. Write a 95% confidence interval for the difference in proportions of people who may find these medications effective. Interpret your interval.

2. Does this interval contain zero? What does that mean?

May you show it me in the handwritten as well as in the calculator (TI-84).

Thank you so much !

Answer 1

a)

  

The critical Z value for a 95% confidence interval is 1.96

So the confidence interval is [0.017, 0.261]

We are 95% confident that the true difference in proportions of people who may find the medications A and B effective lies in the interval [0.017, 0.261]

b)

No, the interval does not contain zero. This means that proportion1 is significantly different than proportion 2.