Question

3. Dr. Lynn 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

Solution,

Given that,

$\hat p$ = 0.5

1 - $\hat p$ = 1 - 0.5 = 0.5

margin of error = E = 3.5% = 0.035

At 90% confidence level

$\alpha$ = 1 - 90%  

$\alpha$ = 1 - 0.90 = 0.10

$\alpha$/2 = 0.05

Z$\alpha$/2 = Z_0.05 = 1.645

sample size = n = (Z_{$\alpha$ / 2} / E )² * $\hat p$ * (1 - $\hat p$ )

= ( 1.645 / 0.035 )² * 0.5 * 0.5

= 552.25

Sample size = n = 552