Questions based on Tables 1:

1. The investigators found out that (not reported in the paper) the prevalence of obesity in the study sample (total sample, n=39) is 20.5%.

a) Calculate and interpret a 95% CI for the prevalence rate in the population where the study sample was selected.

b) Assume that BMI has a normal distribution. Using results for the total sample at baseline:

c) What is the probability that BMI is between 25 and 30?

d) Calculate the 97.5th percentile of BMI

e) Calculate a 95% confidence interval for the population mean of BMI. Interpret the interval.

Total Test p-value VLCKD 14 38.7 (7.1) 39 38.9 (7.1) 0.992 ANOVA Fisher's 0.198 9 (64.3) 5 (35.71) 25 (64.1) 14 (35.9) Fisher's 0.733 Table 1 Baseline characteristics of study participants. Treatment group MCD LCD 12 13 Age mean (SD) 39.1 (6.6) 38.9 (8.3) Gender (%) Female 10 (83.3) 6 (462) Male 2 (16.67) 7 (53.85) Ethnicity (%) Asian 1 (8.3) 0 (0.0) European 8 (66.7) 11 (84.6) Maori 2 (16.7) 1 (7.7) Other ethnicity 1 (8.3) 0 (0.0) Pacific peoples 0 (0.0) 1 (7.7) Total energy (Kcal) mean (SD) 1,435 (293) 1,567 (666) Weight (kg) mean (SD) 76.3 (14.9) 90.4 (20.0) Height (m) mean (SD) 1.70 (0.10) 1.76 (0.08) BMI (kg/m) mean (SD) 26.4 (3.23) 29.1 (4.92) Glucose (mmol/L) mean (SD) 5.54 (0.43) 5.38 (0.47) Total cholesterol (mmol/L) mean (SD) 5.20 (1.3) 4.57 (0.61) Triglyceride (mmol/L) mean (SD) 0.79 (0.2) 0.99 (0.36) Insulin (pmol/L) mean (SD) 63.1 (37.3) 81.1 (39.4) Note: SD, standard deviation; BMI, body mass index. 1 (7.1) 10 (71.4) 3 (21.4) 0 (0.0) 0 (0.0) 1,805 (857) 76.8 (11.2) 1.74 (0.09) 25.5 (2.77) 5.44 (0.44) 6.10 (1.37) 0.92 (0.22) 41.6 (17.6) 2 (5.1) 29 (74.4) 6 (15.4) 1 (2.6) 1 (2.6) 1,603 (649) 81.2 (16.6) 1.73 (0.09) 27.0 (3.96) 5.45 (0.44) 5.31 (1.29) 0.90 (0.27) 61.4 (35.8) 0.378 0.046 0.245 0.050 ANOVA ANOVA ANOVA ANOVA ANOVA ANOVA ANOVA ANOVA 0.673 0.005 0.184 0.012 Total Test p-value VLCKD 14 38.7 (7.1) 39 38.9 (7.1) 0.992 ANOVA Fisher's 0.198 9 (64.3) 5 (35.71) 25 (64.1) 14 (35.9) Fisher's 0.733 Table 1 Baseline characteristics of study participants. Treatment group MCD LCD 12 13 Age mean (SD) 39.1 (6.6) 38.9 (8.3) Gender (%) Female 10 (83.3) 6 (462) Male 2 (16.67) 7 (53.85) Ethnicity (%) Asian 1 (8.3) 0 (0.0) European 8 (66.7) 11 (84.6) Maori 2 (16.7) 1 (7.7) Other ethnicity 1 (8.3) 0 (0.0) Pacific peoples 0 (0.0) 1 (7.7) Total energy (Kcal) mean (SD) 1,435 (293) 1,567 (666) Weight (kg) mean (SD) 76.3 (14.9) 90.4 (20.0) Height (m) mean (SD) 1.70 (0.10) 1.76 (0.08) BMI (kg/m) mean (SD) 26.4 (3.23) 29.1 (4.92) Glucose (mmol/L) mean (SD) 5.54 (0.43) 5.38 (0.47) Total cholesterol (mmol/L) mean (SD) 5.20 (1.3) 4.57 (0.61) Triglyceride (mmol/L) mean (SD) 0.79 (0.2) 0.99 (0.36) Insulin (pmol/L) mean (SD) 63.1 (37.3) 81.1 (39.4) Note: SD, standard deviation; BMI, body mass index. 1 (7.1) 10 (71.4) 3 (21.4) 0 (0.0) 0 (0.0) 1,805 (857) 76.8 (11.2) 1.74 (0.09) 25.5 (2.77) 5.44 (0.44) 6.10 (1.37) 0.92 (0.22) 41.6 (17.6) 2 (5.1) 29 (74.4) 6 (15.4) 1 (2.6) 1 (2.6) 1,603 (649) 81.2 (16.6) 1.73 (0.09) 27.0 (3.96) 5.45 (0.44) 5.31 (1.29) 0.90 (0.27) 61.4 (35.8) 0.378 0.046 0.245 0.050 ANOVA ANOVA ANOVA ANOVA ANOVA ANOVA ANOVA ANOVA 0.673 0.005 0.184 0.012