Sweetness of orange juice. Refer to the orange juice quality study, Exercise 11.26 (p. 642). 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 table below.

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. Run Sweetness Index Pectin (ppm) 1 5.2 220 2 5.5 227 3 6.0 259 4 5.9 210 5 5.8 224 6 6.0 215 7 5.8 231 8 5.6 268 9 5.6 239 10 5.9 212 11 5.4 410 12 5.6 256 13 5.8 306 14 5.5 259 15 5.3 284 16 5.3 383 17 5.7 271 18 5.5 264 19 5.7 227 20 5.3 263 21 5.9 232 22 5.8 220 23 5.8 246 24 5.9 241 Note: The data in the table are authentic. For confidentiality reasons, the manufacturer cannot be disclosed.