Heights of Starting Players. In Example 7.5, we used the definition of the standard deviation of a variable (Definition 3.12 on page 164) 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¯ for samples of sizes 1, 2, 3, 4, and 5. The results are summarized in Table 7.6 on page 337. Because the sampling is without replacement from a finite population, Equation (7.1) can also be used to obtain σx¯.

a. Apply Equation (7.1) to compute σx¯ 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 σx¯ 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?

c. What percentages of the population size are samples of sizes 1, 2, 3, 4, and 5?