Question

# An NHANES report gives data for 644 women aged 20–29 years. The BMI of these 644...

An NHANES report gives data for 644 women aged 20–29 years. The BMI of these 644 women was ?¯= 27 . On the basis of this sample, we want to estimate the BMI ? in the population of all 20.6 million women in this age group. We treated these data as an SRS from a Normally distributed population with standard deviation ?=7.8 . (

a) Suppose we had an SRS of just 90 young women. What would be the margin of error for 95% confidence?

(b) Suppose we had an SRS of 444 young women. What would be the margin of error for 95% confidence?

c) Suppose we had an SRS of 1633 young women. What would be the margin of error for 95% confidence?

(d) Select an explanation that correctly describes how increasing the sample size changes the margin of error of a confidence interval when the confidence level and population standard deviation remain the same.

Margin of error decreases as ? increases.

Margin of error is unaffected by the sample size ? .

Margin of error remains the same as ? increases.

Margin of error increases as ? increases.

Solution:-

N = 644, ?¯= 27, ? = 7.8

a) The margin of error for 95% confidence is 1.6115

n = 90

M.E = 1.96*0.82219

M.E = 1.6115

b) The margin of error for 95% confidence is 0.7255.

n = 444

M.E = 1.96*0.37017

M.E = 0.7255

c) The margin of error for 95% confidence is 0.3783.

n = 1633

M.E = 1.96*0.19302

M.E = 0.3783

d) Margin of error decreases as ? increases.

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