A vision insurance company selects a SRS of 300 clients who wear contact lenses. They randomly assign 200 clients to the experimental group to receive an app that promotes contact lens hygiene. The remaining 100 clients form the control group. Suppose that without the app, 96%, percent of their clients with contact lenses would have healthy eyes for the year, and that with the app, 99%, percent would have healthy eyes.
After a year, the insurance company looks at the difference (Experimental−Control) between the proportions of clients with healthy eyes in each group.
What will be the shape of the sampling distribution of the difference in sample proportions, and why?
A
Approximately normal, because we expect 288 healthy and 12 not-healthy in both groups, and all of these counts are at least 10.
B
Approximately normal, because we expect 192 healthy and 20 not-healthy eyes for the experimental group, and 96 and 40 for the control group, and all of these counts are at least 10.
C
Not normal, because we expect fewer than 10 clients with healthy eyes in both groups.
D
Not normal, because we expect fewer than 10 clients with not-healthy eyes in both groups.