The number of years of education of self-employed individuals in the United States has a population mean of 13.6 years and a population standard deviation of 3.0 years. If we survey a random sample of 100 self-employed people to determine the average number of years of education for the sample, what is the mean of the sampling distribution of x-bar (the sample mean)?
SEm = SD/√n = 3/√100 = 3/10 = .3
sample mean = 13.6 ± .3 (68% of the time)
To find the mean of the sampling distribution of x-bar (the sample mean), we need to note that the mean of the sampling distribution is equal to the population mean. In this case, the population mean is given as 13.6 years.
The mean of the sampling distribution is often denoted as μx-bar, and it represents the average value of the sample means taken from multiple random samples of the same size. In this case, we are considering a random sample of 100 self-employed people.
Since the population mean is equal to the mean of the sampling distribution, the mean of the sampling distribution of x-bar for this particular case is also 13.6 years.
Therefore, the mean of the sampling distribution of x-bar is 13.6 years.