A nurse at a local hospital is interested in estimating the birth weight of infants. How large a sample must she select if she desires to be 98% confident that the true mean is within 4 ounces of the sample mean? The population standard deviation of the birth weights is known to be 5 ounces.
Added by Julia T.
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First, we need to identify the level of confidence, which is 98%. The z-score for a 98% confidence level is approximately 2.33 (you can find this value in a standard z-score table). Show more…
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A newborn baby has extremely low birth weight $(\mathrm{ELBW})$ if it weighs less than 1000 grams. A study of the health of such children in later years examined a random sample of 219 children. Their mean weight at birth was $\overline{x}=810$ grams. This sample mean is an unbiased estimator of the mean weight $\mu$ in the population of all ELBW babies, which means that (a) in all possible samples of size 219 from this population, the mean of the values of $\overline{x}$ will equal 810 . (b) in all possible samples of size 219 from this population, the mean of the values of $\overline{x}$ will equal $\mu .$ (c) as we take larger and larger samples from this population, $\overline{x}$ will get closer and closer to $\mu$ (d) in all possible samples of size 219 from this population, the values of $\overline{x}$ will have a distribution that is close to Normal. (e) the person measuring the children's weights does so without any systematic error.
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