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 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 , the sample mean? 0.3 years 3 years 13.6 years
Mathematics · College · Tue Nov 03 2020
Answered on
The mean of the sampling distribution of the sample mean (denoted as ¯x) is equal to the population mean. This is a fundamental concept in statistics known as the "Central Limit Theorem," which states that the sampling distribution of the sample mean will be normally distributed (if the sample size is sufficiently large) and its mean will be the same as the population mean, regardless of the population's distribution.
Since you've stated that the population mean (μ) is 13.6 years, the mean of the sampling distribution of the sample mean will also be 13.6 years.