Refer to the orange juice quality study, Exercise 11.26. Recall that a manufacturer that has developed a quantitative index of the "sweetness" of orange juice is investigating the relationship between the sweetness index and the amount of water-soluble pectin in the orange juice it produces. The data for 24 production runs at a juice manufacturing plant are reproduced in the next table.

a. Calculate Spearman's rank correlation coefficient between the sweetness index and the amount of pectin. Interpret the result.

b. Conduct a nonparametric test to determine whether there is a negative association between the sweetness index and the amount of pectin. Use a = .01.

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Pectin (ppm) Run Sweetness Index 5.2 5.5 220 227 2 6.0 5.9 5.8 6.0 5.8 259 210 224 215 231 4 268 239 212 410 256 306 5.6 5.6 5.9 5.4 5.6 5.8 9. 10 11 12 13 5.5 5.3 5.3 5.7 259 284 383 271 264 14 15 16 17 18 19 5.5 5.7 5.3 5.9 5.8 5.8 5.9 227 263 232 220 246 241 20 21 22 23 24