A National Health and Nutrition Examination survey (NHANES) report gives data fo

Question

A National Health and Nutrition Examination survey (NHANES) report gives data for 654 women aged 20 to 29 years. The mean BMI of these 6s4 women was x vector = 26.8, Body mass index (BMI) is the weight in kilograms divided by the square of the height of a person in meters. On the basis of this sample, we want to estimate the mean BMI in the population of all 20.6 million women in this age group. If the population standard deviation is sigma = 7.5, a. construct a 97% confidence interval and explain what your confidence interval says in the context of the problem. b. construct a 94% upper confidence bound and explain what your upper confidence bound says in the context of the problem. c. if it is desirable to estimate the mean BMI of all women in this age group with plusminus 0.5 precison and 92% confidence, what sample size would you recommend?

Explanation / Answer

a) here std error of mean =std deviation/(n)1/2 =0.2933

for 97% CI, z=2.1701

hence confidence interval =sample eman +/- z*std error =26.1636 ; 27.4364

above confidence intrerval gives 97% probability to contain true mean of population

b)for 94% CI, z=1.8808

hence confidence interval =sample eman +/- z*std error =26.2484 ; 27.3516

upper bound has 94% probabilty that true population mean does not exceed this value

c)margin of error =0.5

for std deviation =7.5

and for 92% CI, z=1.7507

hence sample size =(Z*std deviation/E)2 =~690 (rounding it up)

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