we have survey data on the body mass index (BMI) of 666 young women. The mean BM

Question

we have survey data on the body mass index (BMI) of 666 young women. The mean BMI in the sample was x = 25·We treated these data as an SRS from a Normally distributed population with standard deviation 8 (a) suppose that we had an SRS of just 84 young women, what would be the margin of error for 95% confidence? (Round your answer to four decimal places.) b) Find the margins of error for 95% confidence based on SR s of 378 young women and 1615 young women. Round your answers to four decimal places. margin of error 378 1615

Explanation / Answer

mean is 25 and s is 8

a) for N=84, the standard error SE is s/sqrt(N)=8/sqrt(84)=0.8729

z for 95% confidence is 1.96, thus the lower bound is mean-z*SE=25-1.96*0.8729=23.289

upper bound is mean+z*SE=25+1.96*0.8729=26.711

b) margin of error for 378 women is z*s/sqrt(N)=1.96*8/sqrt(378)=0.80649

margin of error for 1615 is 1.96*8/sqrt(1615)=0.39018

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