Do these data provide evidence that breast-fed babies have shorter durations of effusion when compared to bottle-fed babies that are the same age, sex, socioeconomic status, and on the same medications? Use the binomial distribution to answer this question and carefully justify your answer. Note: When the paired difference is zero, we drop that observation from the results and adjust n accordingly.

Pair Number Duration of effusion in breast-fed baby Duration of effusion in bottle-fed baby Difference Sign of Difference 1 20 18 -2 - 2 11 35 24 + 3 3 7 4 + 4 24 182 158 + 5 7 6 -1 - 6 28 33 5 + 7 58 223 165 + 8 7 7 0 0 9 39 57 18 + 10 17 76 59 + 11 17 186 169 + 12 12 29 17 + 13 52 39 -13 - 14 14 15 1 + 15 12 21 9 + 16 30 28 -2 - 17 7 8 1 + 18 15 27 12 + 19 65 77 12 + 20 10 12 2 + 21 7 8 1 + 22 19 16 -3 - 23 34 28 -6 - 24 25 20 -5 -