A physician has to prescribe a dose of preventive medicine to all adult women in a town but has to be careful that the dose is not too off from the recomended range according to their BMI. She therefore needs to know the average BMI of the women in town to come up with a single number for the dose of the medicince. In order to get a quick estimate, she measures the BMI of the 6 women who showed up at her clinic on that day and got a number of 22.5. However, the physician knows that she can't just assume this number to be equal to the average BMI of the population. Instead, she looks for the amount of variation of BMI in the 6 patients, computes the sample standard deviation which she finds to be 2.4. She then assumes that the average BMI of women in the town is somewhere between (22.5 – 2.4) = 20.1 and (22.5 + 2.4) = 24.9. Although the physician did not employ a very clear statistical reasoning, show that this is not actually a very bad estimate by computing the confidence level of this interval for the average BMI of the population.
A physician has to prescribe a dose of preventive medicine to all adult women in a town but has to be careful that the dose is not too off from the recomended range according to their BMI. She therefore needs to know the average BMI of the women in town to come up with a single number for the dose of the medicince. In order to get a quick estimate, she measures the BMI of the 6 women who showed up at her clinic on that day and got a number of 22.5. However, the physician knows that she can't just assume this number to be equal to the average BMI of the population. Instead, she looks for the amount of variation of BMI in the 6 patients, computes the sample standard deviation which she finds to be 2.4. She then assumes that the average BMI of women in the town is somewhere between (22.5 – 2.4) = 20.1 and (22.5 + 2.4) = 24.9. Although the physician did not employ a very clear statistical reasoning, show that this is not actually a very bad estimate by computing the confidence level of this interval for the average BMI of the population.
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter7: Applying Fractions
Section7.2: Proportions
Problem 47WE
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Transcribed Image Text:A physician has to prescribe a dose of preventive medicine to all adult women in a town
but has to be careful that the dose is not too off from the recomended range according to
their BMI. She therefore needs to know the average BMI of the women in town to come
up with a single number for the dose of the medicince. In order to get a quick estimate,
she measures the BMI of the 6 women who showed up at her clinic on that day and got a
number of 22.5. However, the physician knows that she can't just assume this number to be
equal to the average BMI of the population. Instead, she looks for the amount of variation
of BMI in the 6 patients, computes the sample standard deviation which she finds to be
2.4. She then assumes that the average BMI of women in the town is somewhere between
(22.5
- 2.4) = 20.1 and (22.5 + 2.4)
= 24.9. Although the physician did not employ a very
clear statistical reasoning, show that this is not actually a very bad estimate by computing
the confidence level of this interval for the average BMI of the population.
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