In a study on diabetes and weight, there were 121 older Americans (55 and older)
ID: 2936976 • Letter: I
Question
In a study on diabetes and weight, there were 121 older Americans (55 and older) who were diabetic and obese or overweight. Those subjects were diagnosed with diabetes by virtue of having an A1C value over 6.5%; the average A1C for those subjects was actually 7.1% with a standard deviation of 0.7%.
a)Find a 90% confidence interval for the average A1C value of all older Americans who are diabetic and obese or overweight. Interpret your interval.
b)Find a 95% confidence interval for the average A1C value of all older Americans who are diabetic and obese or overweight. You do not need to interpret your interval.
c)Find a 99% confidence interval for the average A1C value of all older Americans who are diabetic and obese or overweight. You do not need to interpret your interval.
d)Are the above confidence levels exact or approximate? Why?
e)What sample size is required to estimate the true averageA1C value of all older Americans who are diabetic and obese or overweight to within 0.1% with 95% confidence?
Explanation / Answer
(a)
n = 121
x-bar = 7.1
s = 0.7
% = 90
Standard Error, SE = s/n = 0.7/121 = 0.063636364
Degrees of freedom = n - 1 = 121 -1 = 120
t- score = 1.6576509
Width of the confidence interval = t * SE = 1.65765089984544 * 0.0636363636363636 = 0.105486875
Lower Limit of the confidence interval = x-bar - width = 7.1 - 0.10548687544471 = 6.994513125
Upper Limit of the confidence interval = x-bar + width = 7.1 + 0.10548687544471 = 7.205486875
The 90% confidence interval is [6.99, 7.21]
(b)
n = 121
x-bar = 7.1
s = 0.7
% = 95
Standard Error, SE = s/n = 0.7/121 = 0.063636364
Degrees of freedom = n - 1 = 121 -1 = 120
t- score = 1.979930381
Width of the confidence interval = t * SE = 1.97993038100371 * 0.0636363636363636 = 0.12599557
Lower Limit of the confidence interval = x-bar - width = 7.1 - 0.125995569700236 = 6.97400443
Upper Limit of the confidence interval = x-bar + width = 7.1 + 0.125995569700236 = 7.22599557
The 95% confidence interval is [6.97, 7.23]
(c)
n = 121
x-bar = 7.1
s = 0.7
% = 99
Standard Error, SE = s/n = 0.7/121 = 0.063636364
Degrees of freedom = n - 1 = 121 -1 = 120
t- score = 2.617421135
Width of the confidence interval = t * SE = 2.61742113517857 * 0.0636363636363636 = 0.166563163
Lower Limit of the confidence interval = x-bar - width = 7.1 - 0.166563163147727 = 6.933436837
Upper Limit of the confidence interval = x-bar + width = 7.1 + 0.166563163147727 = 7.266563163
The 99% confidence interval is [6.93, 7.27]
(d) These intervals are approximate
(e) z- score for 95% confidence is z = 1.96
N = (z * /E)^2 = (1.96 * 0.7/0.1)^2 = 189
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.