Question

# 2.        An NHANES report gives data for 654 women aged 20 to 29 years. The mean...

2.        An NHANES report gives data for 654 women aged 20 to 29 years. The mean BMI for these 654 women was x = 26.8. On the basis of this sample, we are going to estimate the mean    BMI μ in the population of all 20.6 million women in this age group. We will assume that the NHANES sample is a SRS from a normal distribution with known standard deviation σ = 7.5

a) Construct 3 confidence intervals for the mean BMI m in this population using 90%, 95%, and 99% confidence.

b) What are the margin of errors for 90%, 95% and 99% confidence.

c) How does increase in confidence level change the margin of error when the sample size and population standard deviation remain the same?

d) Suppose we have a SRS of just 100 young women. What would the margin of error for 95% confidence?

e) Find the margin of error for 95% confidence based on SRSs of 400 young women.

f) Find the margin of error for 95% confidence based on SRSs of 1600 young women.

g) Compare the three margin of errors. How does the increase in sample size change the margin of error when the confidence level and population standard deviation remain the same.

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