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Example 8.1 Cholesterol Reduction Study (Confidence Interval) Clinical trials are conducted to compare the difference in effectiveness of drugs in lower- ing cholesterol levels, blood pressure, cancer recurrence, and numerous other medical conditions. Suppose that one research team is studying the effectiveness of two drugs to reduce cholesterol levels. In order to control variation in reduction that might be due to factors other than the drug itself, a matched pair sample design is selected. Each mem- ber of a pair is matched by age, weight, lifestyle, and other pertinent factors. Drug X is tested by one person randomly selected from each pair, and drug Y is tested by the other individual in the pair. After a specified amount of time, each person's cholesterol level is measured again. Although clinical studies may involve many hundreds or even thou- sands of participants, we simply illustrate the matched-pair statistical procedure for dependent samples in Example 8.1 with a very small random sample of pairs of partici- pants with known cholesterol problems. Table 8.1 gives the number of points by which each person's cholesterol level was reduced as well as the differences, d, = x; - Yi, for each pair. Notice the missing value in pair 5. Estimate with a 99% confidence level the mean difference in the effectiveness of the two drugs, X and Y, to lower cholesterol. Table 8.1 Cholesterol Reduction PAIR DRUG X DRUG Y DIFFERENCE (d; = x; y:) 3 5 1 26 29 32 27 2 3 28 LOO k11 4 27 4 5 5 31 32 30 32 29 31 6 2 30 26 7 3 8 33 -2 9 30 36 -6