Question

Dr. Schommer has a new skin cream that she believes will cure a common skin ailment. She wants to conduct a study to test this new skin cream to know what proportion of the population it might help, but knows that choosing an appropriate sample size is important. She wants to be within 3.5 percentage points with 90% confidence.

a. Since this is the first study Dr. Schommer is doing for this new skin cream, explain why it’s appropriate for her to assume a point estimate of 0.5. (4 points)

b. What is the minimal sample size she should use in her study? (8 points)

Answer 1

a) As we dont have a prior proportion value here, and the margin of error here is computed as:

To be conservative value of sample size, we use the value of proportion p which maximizes the value of n. That is done here by maximizing K = p(1-p)

K is maximized for p = 0.5. Therefore 0.5 is the required value here.

b) The margin of error here is computed as:

The sample size here is computed as:

Therefore 553 is the required sample size here.