An NHANES report gives data for 652 women aged 20 – 29 20–29 years. The BMI of these 652 652 women was ¯ x = 26.5 x¯= 26.5 . On the basis of this sample, we want to estimate the BMI μ μ in the population of all 20.6 20.6 million women in this age group. We treated these data as an SRS from a Normally distributed population with standard deviation σ = 7.2 σ=7.2 . Give three confidence intervals for the mean BMI μ in this population, using 90%, 95%, and 99% confidence. Enter the lower and upper bound for the 90% confidence interval.

Accepted Solution

Answer:Lower bound of 90% confidence interval: 26.04Upper bound of 90% confidence interval: 26.96Step-by-step explanation:We are given the following in the question:  Sample mean, [tex]\bar{x}[/tex] = 26.5Sample size, n = 652Population standard deviation, σ = 7.290% Confidence interval: [tex]\mu \pm z_{critical}\frac{\sigma}{\sqrt{n}}[/tex] Putting the values, we get, [tex]z_{critical}\text{ at}~\alpha_{0.05} = 1.645[/tex] [tex]26.5 \pm 1.645(\frac{7.2}{\sqrt{652}} ) = 26.5 \pm 0.4638 =(26.0362,26.9638) \approx (26.04,26.96)[/tex]