Final answer:
The standard error for the concentration of nickel in Nigerian coins is calculated based on the mean and standard deviation of the sample measurements. It quantifies the dispersion in the sample and is used to estimate the accuracy of the sample mean representing the population mean.
Step-by-step explanation:
To calculate the standard error for the concentration of nickel in Nigerian coins, we must first calculate the mean (average) and the standard deviation of the provided measurements. The measurements in milligrams are: 3.65, 4.11, 3.59, 7.31, 3.95, 3.87, 4.06, 1.48, 3.60, 3.76, and 3.99. Adding these together and dividing by the number of measurements gives us the mean. To find the standard deviation, we calculate the sum of the squared differences from the mean for each measurement, divide by the number of measurements minus one, and then take the square root of this value. Finally, the standard error is the standard deviation divided by the square root of the number of measurements.
The mean calculated from the given measurements is 3.92 milligrams, and the standard error is a way to quantify the amount of variation or dispersion of a set of values. A low standard error suggests that the sample mean is a more accurate reflection of the actual population mean. The standard error is particularly useful as a means to calculate confidence intervals around the mean for a set of scores.