The correct answer is: C. the sample variance divided by the sample mean.
The standard error is a measure of how much variability there is in a sample statistic. It is calculated by taking the square root of the sample variance divided by the sample size. The sample variance is a measure of how spread out the data points are in a sample. It is calculated by taking the sum of the squared deviations from the mean and dividing by the number of data points minus 1. The sample mean is the average of the data points in a sample. It is calculated by adding up all the data points and dividing by the number of data points.
The standard error is used to estimate the standard deviation of the population from which the sample was taken. The standard deviation is a measure of how spread out the data points are in a population. It is calculated by taking the square root of the variance. The variance is a measure of how much variability there is in a population. It is calculated by taking the sum of the squared deviations from the mean and dividing by the number of data points.
The standard error is also used to construct confidence intervals. A confidence interval is a range of values that is likely to contain the true value of the population parameter. The confidence interval is calculated by taking the sample statistic plus or minus the standard error times the critical value. The critical value is a value that depends on the confidence level. The confidence level is the probability that the confidence interval contains the true value of the population parameter.
Here is a brief explanation of each option:
- Option A: The sample variance divided by the total number of sample instances. This is not the correct answer because the standard error is not equal to the sample variance divided by the total number of sample instances. The standard error is equal to the square root of the sample variance divided by the sample size.
- Option B: The population variance divided by the total number of sample instances. This is not the correct answer because the standard error is not equal to the population variance divided by the total number of sample instances. The standard error is equal to the square root of the sample variance divided by the sample size.
- Option C: The sample variance divided by the sample mean. This is the correct answer because the standard error is equal to the square root of the sample variance divided by the sample size.
- Option D: The population variance divided by the sample mean. This is not the correct answer because the standard error is not equal to the population variance divided by the sample mean. The standard error is equal to the square root of the sample variance divided by the sample size.