QuestionAn NHANES report gives data for 641 men aged $20-29$ years. The BMI of these 641 men was $\bar{x}=25.6$. On the basis of this sample, we want to estimate the BMI $\mu$ in the population of all 23.2 million American men in this age group. Treat these data as an SRS from a Normally distributed population with standard deviation $\sigma=7.2$.
Source adapted from: Adapted from Fryar C. D., et al., Anthropometric reference data for children and adults: United States, 2011-2014. National Center for Health Statistics. Vital Health Statistics 3(2016), at htips:/www. ode.gov/nchs/data/ series/mr_04sr03_039.pAf.
Compare the three margins of error. How does increasing the sample size change the margin of error of a confidence interval when the confidence level and population standard deviation remain the same? Margin of error remains the same as $n$ increases. Margin of error is unaffected by the sample size $n$. Margin of error increases as $n$ increases. Margin of error decreases as $n$ increases.