In Example 7.5, we used the definition of the standard deviation of a variable (Definition 3.12 on page 130) to obtain the standard deviation of the heights of the five starting players on a men's basketball team and also the standard deviation of x-bar for samples of sizes 1, 2, 3, 4, and 5. The results are summarized in Table 7.6 on page 287. Because the sampling is without replacement from a finite population, Equation (7.1) can also be used to obtain σx-bar.
a. Apply Equation (7.1) to compute σx-bar for samples of sizes 1, 2, 3, 4, and 5. Compare your answers with those in Table 7.6.
b. Use the simpler formula, Equation (7.2), to compute σ. x for samples of sizes 1, 2, 3, 4, and 5. Compare your answers with those in Table 7.6. Why does Equation (7.2) generally yield such poor approximations to the true values?