A study of the health of teenagers plans to measure the blood cholesterol levels of an SRS of 13- to 16-year-olds. The researchers will report the mean bar (x) from their sample as an estimate of the mean cholesterol level in this population. What does it mean to say that bar (x) is an unbiased estimator of mu ' If we chose many SRSs and calculated the sample mean bar (x) for each sample, the distribution of bar (x) would be centered at the value of mu . This means that in repeated simple random samples from the same population the value of the sample mean will vary. This means that the mean of the population will always be close to the value of the sample mean. If we select an SRS and calculate the sample mean, the sample mean will equal mu .

To say that $\bar{x}$ is an unbiased estimator of $\mu$ means that the expected value of the sample mean $\bar{x}$ is equal to the population mean $\mu$. In other words, if we were to take many simple random samples (SRSs) from the same population and calculate the sample mean for each sample, the distribution of these sample means would be centered at the value of the population mean $\mu$.<br /><br />This means that in repeated simple random samples from the same population, the value of the sample mean will vary, but the average of these sample means will be equal to the population mean $\mu$. It does not mean that the sample mean will always be exactly equal to the population mean for a single sample, but rather that the sample mean is an accurate estimate of the population mean on average.<br /><br />Therefore, the correct statement is: "If we chose many SRSs and calculated the sample mean $\bar{x}$ for each sample, the distribution of $\bar{x}$ would be centered at the value of $\mu$."