Question

ch 15 an srs of 25 recent birth records at the local hospital was selected. in the sample, the average birth weight was $\bar{x}=119.6$ ounces. suppose the standard deviation is known to be $sigma = 6.5$ ounces. assume that in the population of all babies born in this hospital, the birth weights follow a normal distribution, with mean $mu$. if the sample size of birth records increases, how does the sampling distribution change? the sampling distribution will remain normal and the mean will remain the same regardless of the sample size, but its standard deviation will be smaller than the sampling distribution based on the smaller sample. the shape of the distribution will change, but it is not possible to determine what the new distribution will be without knowing the new data. the sampling distribution will remain normal regardless of the sample size, and will have the same average and standard deviation as the sampling distribution computed from the smaller sample. the shape of the distribution will change, but it is dependent upon the new data that is collected.

Explanation:

When the population is normally - distributed, the sampling distribution of the sample mean is also normally - distributed for any sample size. The mean of the sampling distribution of the sample mean is equal to the population mean $\mu$, which remains constant regardless of the sample size. The standard deviation of the sampling distribution of the sample mean (also known as the standard error) is given by $\frac{\sigma}{\sqrt{n}}$, where $\sigma$ is the population standard deviation and $n$ is the sample size. As $n$ increases, $\frac{\sigma}{\sqrt{n}}$ decreases.

Answer:

The sampling distribution will remain Normal and the mean will remain the same regardless of the sample size, but its standard deviation will be smaller than the sampling distribution based on the smaller sample.