The quality of the orange juice produced by a manufacturer is constantly monitored. There are numerous sensory and chemical components that combine to make the​ best-tasting orange juice. For​ example, one manufacturer has developed a quantitative index of the​ "sweetness" of orange juice. Suppose a manufacturer wants to use simple linear regression to predict the sweetness​ (y) from the amount of pectin​ (x). Find a 90​% confidence interval for the true slope of the line. Interpret the result.
Click the icon to view the data collected on these two variables during 24 production runs at a​ juice-manufacturing plan:
Run Sweetness Index Pectin (ppm)
1 5.2 220
2 5.5 226
3 6 258
4 5.9 210
5 5.8 224
6 6 215
7 5.8 231
8 5.6 269
9 5.6 239
10 5.9 212
11 5.4 410
12 5.6 254
13 5.7 309
14 5.5 259
15 5.3 284
16 5.3 383
17 5.6 271
18 5.5 264
19 5.7 226
20 5.3 263
21 5.9 234
22 5.8 220
23 5.8 243
24 5.9 241
A. A 90% confidence interval for the true slope of the line is (?,?) ​(Round to four decimal places as​ needed.)
B. interpret the result practically. Select the correct choice below and fill in the answer boxes to complete your choice.
a. We can be 90​% confident that the true mean increase in sweetness index per 1 ppm increase in pectin is between ? and n?. This inference is meaningful for levels of pectin between ? and ? ppm.
b. We can be 90​% confident that the true mean increase in pectin per 1 unit increase in sweetness index is between ? and ? ppm. This inference is meaningful for sweetness levels between ? and ?.