Question

5. A clinician notices in her sample that 28 out of 80 males are obese, compared to 11 out of 50 females, and she constructs a 95% CI for the male minus female difference in proportion obese. Which of the following is the estimated standard error (SB) for the difference in proportions? ( Hint: you need to average males and females)

a. none of the above

b. 0.130

c. 0.079

d. 0.101

6. Which of the following is the lower limit of a 95% CI for the male minus female difference in proportion obese, based on the data in (5)?

a. 0.130

b. 0.285

c. -0.285

d. -0.025

7. Assuming the null hypothesis that the proportion obese among males equals the proportion obese among female in the population, what is the most appropriate SE for the difference in proportions under H0?

a. 0.079

b. 0.083

c. 0.130

d. 0.300

Answer 1

Answer 5)

We have been provided with the following information about the sample proportions:

Standard Error = sqrt(p̂1(1-p̂1)/n1 + p̂2*(1-p̂22/n2)

Standard Error = sqrt(0.35*(1-0.35)/80 + 0.22*(1-0.22)/50)

Standard Error (SE) = 0.079 (Option C)

Answer 6)

The critical value for α=0.05 is zc ​= z1−α/2​ =

Margin of Error ME = zc*SE = 1.96*0.079

ME = 0.155

Lower Limit = p̂1-p̂2 - ME = (0.35-0.22) - 0.155

Lower Limit = -0.025 (Option D)

Answer 7)

Poopled Proportion p = (x1+x2)/(n1+n2) = (28+11)/(80+50) = 0.3

Standard Error = sqrt(p*(1-p)*(1/n1+1/n2)) = sqrt(0.3*(1-0.3)*(1/80+1/50))

Standard Error = 0.083 (Option B)