A newborn baby has extremely low birth weight 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 who had been born with extremely low birth weights. Their mean weight at birth was 810 grams.
a) What is the population being sampled in this study? b) Is 810 a parameter or a statistic? Explain why.



Answer :

A) The population being sampled in this study is Population Mean

B) A parameter or a statistic of 810 is sample mean weight of the children will be same as the mean weight of the population

What is Sample and Population?

The entire group about whom you want to make conclusions is referred to as a population. The particular group from which you will gather data is known as a sample.

Reason For (A) - An objective estimator of the mean weight m in the population of infants with exceptionally low birth weights is the sample mean. This indicates that the sample mean is the same as the population mean when the sample is a straightforward random sample taken from the population.

Reason For (B) - According to the query, a newborn is considered to have a very low birth weight if its weight is less than 1000 grams. 219 infants with extremely low birth weights had an average weight of 810 grams. Additionally, the sample mean provides a fair estimate of the average weight of the population of infants who were born with exceptionally low birth weights.

Therefore, if various samples of size 219 are drawn from the same population, the mean of the sample mean weight of the children will be the same as the mean weight of the population.

The mean of all sample means will be equal to the population mean weight if the ith sample's mean weight is x.

Therefore, the sample mean is an unbiased estimator of the population mean, which means that when various samples of size 219 are drawn from the same population, the mean of the sample means will be identical to the population mean.

A) The population being sampled in this study is Population Mean

B) A parameter or a statistic of 810 is sample mean weight of the children will be same as the mean weight of the population

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