Researchers want to test a new hand exercise plan for arthritis patients to see if they have improved flexibility. They recruited 110 patients with arthritis in their hands and randomly assigned them to one of two treatment groups: group 1 took their regular medicine and did the new hand exercises; and group 2 only took medicine. After one month, 42 of the 55 in group 1 improved in their flexibility, and 37 of the 55 in group 2 improved their flexibility.

Check the conditions for constructing a confidence interval for the difference in proportions.

Random condition:

10% condition:

Large Counts condition:

Are all the conditions for inference met?
✔ Yes