Suppose that the ages of students at a particular university average 26 years with a standard deviation of 2.8 years. Consider the sampling distribution of the sample mean age of students in a sample of n = 49. The standard deviation of the sampling distribution is
To find the standard deviation of the sampling distribution of the sample mean age, we need to use the formula:
Standard Deviation of Sampling Distribution = Standard Deviation of the Population / Square Root of Sample Size
In this case, the Standard Deviation of the Population is given as 2.8 years and the Sample Size is 49.
So, substituting the values into the formula, we get:
Standard Deviation of Sampling Distribution = 2.8 / √49
Now we can calculate the standard deviation:
Standard Deviation of Sampling Distribution = 2.8 / 7
Simplifying the equation, we can find that:
Standard Deviation of Sampling Distribution = 0.4 years
Therefore, the standard deviation of the sampling distribution is 0.4 years.