A large corporation employs 27,251 individuals. The average income in 2008 for all employees was $74,550 with a standard deviation of $19,872. You are interested in comparing the incomes of today’s employees with those of 2008. A random sample of 100 employees of the corporation yields = +75,207 and s = +18,901.
a. Describe the center and variability of the population distribution. What shape does it probably have? Explain.
b. Describe the center and variability of the data distribution. What shape does it probably have? Explain.
c. Describe the center and variability of the sampling distribution of the sample mean for n = 100. What shape does it have? Explain.
d. Explain why it would not be unusual to observe an individual who earns more than $100,000, but it would be highly unusual to observe a sample mean income of more than $100,000 for a random sample size of 100 people.