a distribution of scores has 6, but the value of the mean is unknown, a researcher plans to select a sample from the population in order to learn more about the unknown mean, if the sample consist of n= 9 scores , how accurately should sample mean represent the population mean

The accuracy of the sample mean in representing the population mean depends on several factors, such as the variability (or dispersion) of the scores in the population and the sample size.

In this case, since the value of the mean is unknown, we cannot directly determine the accuracy of the sample mean without further information. However, we can discuss how sample size affects the accuracy of the sample mean.

Generally, as the sample size increases, the sample mean tends to be a more accurate estimate of the population mean. This is because larger samples provide more information about the underlying population and reduce the impact of random sampling errors.

One common way to quantify the accuracy of a sample mean is by calculating the standard error of the mean (SEM). The SEM is an estimate of the standard deviation of the sample mean and is calculated using the formula:

SEM = standard deviation / square root of sample size

By calculating the SEM, we can determine the average amount of error expected between the sample mean and the population mean. A smaller SEM indicates a higher accuracy of the sample mean in representing the population mean.

In summary, to improve the accuracy of the sample mean in representing the population mean, researchers should aim for a larger sample size. This helps to reduce the impact of random sampling errors and provides a more reliable estimate of the population mean.