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A newborn baby has extremely low birth weight (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 bar (x)=810grams. This sample mean is an unbiased estimator of the mean weight mu in the population of all ELBW babies, which means that as we take larger and larger samples from this population, bar (x) will get closer and closer to mu . in all possible samples of size 219 from this population, the values of bar (x) will have a distribution that is close to Normal. in all possible samples of size 219 from this population, the mean of the values of bar (x) will equal 810. in all possible samples of size 219 from this population, the mean of the values of bar (x) will equal mu .

Problemas

A newborn baby has extremely low birth weight (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 bar (x)=810grams. This sample mean is an unbiased estimator of the mean weight mu in the population of all ELBW babies, which means that as we take larger and larger samples from this population, bar (x) will get closer and closer to mu . in all possible samples of size 219 from this population, the values of bar (x) will have a distribution that is close to Normal. in all possible samples of size 219 from this population, the mean of the values of bar (x) will equal 810. in all possible samples of size 219 from this population, the mean of the values of bar (x) will equal mu .

A newborn baby has extremely low birth weight (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 bar (x)=810grams. This sample mean is an unbiased estimator of the mean weight mu in the population of all ELBW babies, which means that as we take larger and larger samples from this population, bar (x) will get closer and closer to mu . in all possible samples of size 219 from this population, the values of bar (x) will have a distribution that is close to Normal. in all possible samples of size 219 from this population, the mean of the values of bar (x) will equal 810. in all possible samples of size 219 from this population, the mean of the values of bar (x) will equal mu .

Solución

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Robertoélite · Tutor durante 8 años
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The correct answer is: in all possible samples of size 219 from this population, the mean of the values of $\bar {x}$ will equal $\mu.$<br /><br />Explanation: The statement that the sample mean is an unbiased estimator of the mean weight $\mu$ in the population of all ELBW babies means that the expected value of the sample mean is equal to the population mean. In other words, if we were to take many samples of size 219 from this population and calculate the sample mean for each sample, the average of these sample means would be equal to the population mean $\mu$. This property is known as the unbiasedness of the sample mean.
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