SOLUTION: The following are body mass index (BMI) scores measured in 12 patients who are free of diabetes and are participating in a study of risk factors for obesity. Body mass index is mea

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Question 1191675: The following are body mass index (BMI) scores measured in 12 patients who are free of diabetes and are participating in a study of risk factors for obesity. Body mass index is measured as the ratio of weight in kilograms to height in meters squared. Generate a 95% confidence interval estimate of the true BMI.
28 21 37 38 24 28 38 47 27 32 36 43
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

n = 12 = sample size

Because n > 30 is not true, and because we don't know sigma, we must use the T distribution.

df = degrees of freedom
df = n-1
df = 12-1
df = 11

Use a table or T calculator to determine the critical T value is roughly t = 2.201
This only applies when df = 11 and we have a 95% confidence level.

Use your calculator to compute the following
xbar = sample mean = 33.25
s = sample standard deviation = 7.87545
These two values are based on the original data set of course.
I recommend using spreadsheet software.

E = margin of error
E = t*s/sqrt(n)
E = 2.201*7.87545/sqrt(12)
E = 5.00386

L = lower boundary
L = xbar - E
L = 33.25 - 5.00386
L = 28.24614
L = 28.25

U = upper boundary
U = xbar + E
U = 33.25 + 5.00386
U = 38.25386
U = 38.25

Answer: (28.25, 38.25)
This is in the format (L, U)
This is equivalent to writing 28.25 < mu < 38.25 which is in the format L < mu < U
Another way to write the confidence interval is