(7.1) VN - 1 (7.2)
Bachelor’s Completion. As reported by the U.S. Census Bureau in Educational Attainment in the United States, the percentage of adults in each state who have completed a bachelor’s degree is provided on theWeissStats site. Use the technology of your choice to solve the following problems.
a. Obtain the standard deviation of the variable “percentage of adults who have completed a bachelor’s degree” for the population of 50 states.
b. Consider simple random samples without replacement from the population of 50 states. Strictly speaking, which is the correct formula for obtaining the standard deviation of the sample mean— Equation or Equation? Explain your answer.
c. Referring to part (b), obtain σ x for simple random samples of size 30 by using both formulas. Why does Equation (7.2) provide such a poor estimate of the true value given by Equation (7.1)?
d. Referring to part (b), obtain σ x for simple random samples of size 2 by using both formulas. Why does Equation (7.2) provide a somewhat reasonable estimate of the true value given by Equation (7.1)?
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