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. Run Sweetness Index Pectin (ppm) 1 5.2 220 2 5.5 226 3 6.0 258 4 5.9 210 5 5.8 224 6 6.0 215 7 5.8 234 8 5.6 269 9 5.6 239 10 5.9 212 11 5.4 410 12 5.6 253 13 5.8 307 14 5.5 259 15 5.3 284 16 5.3 383 17 5.7 271 18 5.5 264 19 5.7 226 20 5.3 263 21 5.9 233 22 5.8 220 23 5.8 244 24 5.9 241 Click the icon to view the data collected on these two variables during 24 production runs at a juice-manufacturing plant. A 90% confidence interval for the true slope of the line is (enter your response here,enter your response here). (Round to four decimal places as needed.) Choose the correct answer below. A. We are 10% confident that the change in the mean sweetness index for each one unit change in the pectin is between the limits of the confidence interval. B. We are 90% confident that the change in the mean sweetness index for each one unit change in the pectin is between the limits of the confidence interval. C. We are 90% confident that the change in the mean sweetness index for each one unit change in the pectin is not between the limits of the confidence interval.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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.

Run Sweetness Index Pectin (ppm)
1 5.2 220
2 5.5 226
3 6.0 258
4 5.9 210
5 5.8 224
6 6.0 215
7 5.8 234
8 5.6 269
9 5.6 239
10 5.9 212
11 5.4 410
12 5.6 253
13 5.8 307
14 5.5 259
15 5.3 284
16 5.3 383
17 5.7 271
18 5.5 264
19 5.7 226
20 5.3 263
21 5.9 233
22 5.8 220
23 5.8 244
24 5.9 241

Click the icon to view the data collected on these two variables during 24 production runs at a juice-manufacturing plant.

A 90% confidence interval for the true slope of the line is

(enter your response here,enter your response here).

(Round to four decimal places as needed.)

Choose the correct answer below.

We are 10% confident that the change in the mean sweetness index for each one unit change in the pectin is between the limits of the confidence interval.

We are 90% confident that the change in the mean sweetness index for each one unit change in the pectin is between the limits of the confidence interval.

We are 90% confident that the change in the mean sweetness index for each one unit change in the pectin is not between the limits of the confidence interval.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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