Question

Suppose we have a sample of five values of hemoglobin A1c (HgbA1c) obtained from diabetic patients. The values are 8.5%, 9.3%, 7.9%, 9.2% and 10.3%. Derive a 95% CI for the underlying mean HgbA1c. Suppose that diabetic patients with an underlying mean HgbA1c < 8% are considered in good compliance. How do you evaluate the compliance of patients?

Answer 1

(a)

From the given data, the following statistics are calculated:

n = Sample Size = 5

= Sample Mean = 45.2/5 = 9.04

s = Sample SD = 0.9044

SE = s/

= 0.9044/ = 0.4045

= 0.05

ndf = 5 - 1 = 4

From Table, critical values of t = 2.7764

Confidence interval:

t SE

= 9.04 (2.7764 X 0.4045)

= 9.04 1.1231

= (7.9169 , 10.1631)

So,

95% CI for the underlying mean HgbA1c is given by:

7.9169 % < <10.1631 %

(b)

It is noted that almost all points of the Confidence Interval are greater than 8%, we conclude that the patients are not in good compliance.