Chapter 15.7, Problem 15.78ACI

Sweetness of orange juice Refer to the orange juice quality study, Exercise 11.260 (p. 632). 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

1. a. Calculate Spearman's rank correlation coefficient between the sweetness index and the amount of pectin. Interpret the result.
2. b. Conduct a nonparametric test to determine whether there is a negative association between the sweetness index and the amount of pectin. Use α= .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.