Ladson et al. (2011) conducted a study to estimate racial disparities in the polycystic ovary syndrome (PCOS) phenotype between white and black women with PCOS. The study sample included 120 women with PCOS (77 white and 43 black) and 122 controls (35 white and 87 black). In this sample, the distribution of BMI for black women with PCOS was approximately bell-shaped with a mean of 39.0 kg/m2 and a standard deviation of 9.3 kg/m2. You need to construct a 95% confidence interval for the mean BMI of black women with PCOS. To help you do so, answer each of the following questions.

2. What is the standard error? (1 point)

a. 0.22

b. 1.02

c. 1.42

d. 2.91

e. 9.30

3. What is the critical value? (1 point)

a. 1.645

b. 1.682

c. 1.960

d. 2.000

e. 2.018

4. What is the margin of error? (1 point)

a. 0.44

b. 1.42

c. 2.02

d. 2.86

e. 18.77

5. What is the 95% confidence interval? Provide an appropriate interpretation of this confidence interval. (2 points)

a. There is a 95% chance that the true mean BMI of black women with PCOS will fall within the interval (36.1, 41.9).

b. There is a 95% chance that the true mean BMI of black women with PCOS will fall within the interval (37.6, 40.4).

c. We are 95% confident that the interval (36.1, 41.9) actually does contain the true value of the mean BMI of black women with PCOS.

d. We are 95% confident that the interval (37.6, 40.4) actually does contain the true value of the mean BMI of black women with PCOS.

e. Both a and c are correct.

f. Both b and d are correct.