Question

A simple random sample of six values had mean x(with a line over it)=13.00 and standard deviation =7.155. Calculate the standard error of the sample mean, SE. Give your answer to three decimal places.

Answer 1

The standard error of the sample mean, SE, is a measure of how much the sample mean is expected to vary from the population mean. It is calculated by dividing the standard deviation of the sample by the square root of the sample size. In this case, the standard error of the sample mean is approximately 2.92.

Step-by-step explanation:

The standard error (SE) of the sample mean is a measure of how much the sample mean is expected to vary from the population mean. It is calculated by dividing the standard deviation of the sample by the square root of the sample size. In this case, the standard deviation of the sample mean, SE, is equal to the standard deviation of the sample divided by the square root of the sample size:

SE = standard deviation / √(sample size)

Given that the standard deviation of the sample is 7.155 and the sample size is 6, we can calculate the standard error as:

SE = 7.155 / √(6)

SE ≈ 7.155 / 2.449 = 2.92 (rounded to three decimal places).