Question

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?

(Enter your answer rounded to four decimal places.)

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.

Answer 1

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.