EXAMPLE 6.27 Choosing Sample Size for a Desired Power

CASE 6.1 Suppose the bottler Bestea desires a power of 0.9 in the detection of the specific alternative of . From Example 6.26, we found that a sample size of 20 offers a power of only 0.37. Manually, we can repeat the calculations found in Example 6.26 for different values of larger than 20 until we find the smallest sample size giving at least a power of 0.9. Fortunately, most statistical software saves us from such tedium. Figure 6.19 shows Minitab output with inputs of 0.9 for power, 1% for sig-nifcance level, 2 for , and for the departure amount from the null hypothesis. From the output, we learn that a sample size of at least 60 is needed to have a power of at least 0.9. If we used a sample size of 59, the actual power would be a bit less than the target power of 0.9.

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