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

Question

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.

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Eden 1 week 2021-09-15T18:07:42+00:00 1 Answer 0

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    2021-09-15T18:08:52+00:00

    Answer:

    Lower bound of 90% confidence interval: 26.04

    Upper bound of 90% confidence interval: 26.96

    Step-by-step explanation:

    We are given the following in the question:  

    Sample mean, \bar{x} = 26.5

    Sample size, n = 652

    Population standard deviation, σ = 7.2

    90% Confidence interval:

    \mu \pm z_{critical}\frac{\sigma}{\sqrt{n}}

    Putting the values, we get,

    z_{critical}\text{ at}~\alpha_{0.05} = 1.645

    26.5 \pm 1.645(\frac{7.2}{\sqrt{652}} ) = 26.5 \pm 0.4638 =(26.0362,26.9638) \approx (26.04,26.96)

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27:3+15-4x7+3-1=? ( )