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 mean of the sampling distribution is __________

Hint:

The mean of the sampling distribution is the population mean.

3.174 .800

3.714 To determine the mean of the sampling distribution, we need to recall two important properties.

1. The mean of the sampling distribution of the sample mean is equal to the mean of the population, which in this case is 26 years.

2. The standard deviation of the sampling distribution of the sample mean can be calculated using the formula: standard deviation of the population divided by the square root of the sample size.

Given that the population standard deviation is 2.8 years and the sample size is 49, we can substitute these values into the formula to find the standard deviation of the sampling distribution:

standard deviation of the sample mean = 2.8 / √49

Using the formula, we find:

standard deviation of the sample mean = 2.8 / 7 = 0.4 years

Now, we know that the mean of the sampling distribution is equal to the mean of the population, which is 26 years.

Therefore, the mean of the sampling distribution is 26 years.