Question: 14.5 Sample size and margin of error. Example 13.1 (page 232) described NHANES sur vey data on the body mass index (BMl) of 654 young

14.5 Sample size and margin of error. Example 13.1 (page 232) described NHANES sur vey data on the body mass index (BMl) of 654 young women. The mean BMl in the sample was x = 26.8. We treated these data as an SRS from a Normally distributed pop ulation with standard deviation cr = 7.5.

(a) Suppose that we had an SRS of just 100 young women. What would be the margin of error for 95% confidence?

(b) Find the margins of error for 95% confidence based on SRSs of 400 young women and 1600 young women.

(c) 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?

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