The U.S. Department of Health and Human Services publishes information on AIDS in Morbidity and Mortality Weekly Report. During one year, the number of provisional cases of AIDS for each of the 50 states are as presented on the WeissStats CD. Use the technology of your choice to solve the following problems.
a. Obtain the standard deviation of the variable "number of provisional AIDS cases" 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 (7.1) or Equation (7.2)? 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)?
e. For simple random samples without replacement of sizes 1- 50, construct a table to compare the true values of σ. x- obtained by using Equation (7.1)-with the values of σ. x obtained by using Equation (7.2). Discuss your table in detail.