Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 9, Problem 79SE
The article “The Accuracy of Stated Energy Contents of Reduced-Energy, Commercially Prepared Foods” (J. of the Amer. Dietetic Assoc., 2010: 116–123) presented the accompanying data on vendor-stated gross energy and measured value (both in kcal) for 10 different supermarket convenience meals):
| Meal: | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Stated: | 180 | 220 | 190 | 230 | 200 | 370 | 250 | 240 | 80 | 180 |
| Measured: | 212 | 319 | 231 | 306 | 211 | 431 | 288 | 265 | 145 | 228 |
Carry out a test of hypotheses to decide whether the true average % difference from that stated differs from zero. [Note: The article stated “Although formal statistical methods do not apply to convenience samples, standard statistical tests were employed to summarize the data for exploratory purposes and to suggest directions for future studies.”]
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Suppose that we want to compare the cholestrol contents of four competing diet foods on the basis of the following data (in milligrams per package) which were obtained for three 6-ounce packages of each of the diet foods:
Diet food A: 3.6 4.1 4.0 Diet food B: 3.1 3.2 3.9 Diet food C: 3.2 3.5 3.5 Diet food D: 3.5 3.8 3.8
Fill in the blanks below.
Test at the 0.05 level of significance whether the differences among means obtained for the four competing diet foods (Diet A, B, C, D) are significant? (Ftable=4.07)
source of varation
degrees of freedom
sum of squares
mean squares
F
treatments
?
0.54
?
?
error
?
?
?
total
?
1.18
The accompanying data set consists of observationson shower-flow rate (L/min) for a sample of n 5 129houses in Perth, Australia (“An Application of BayesMethodology to the Analysis of Diary Records in aWater Use Study,” J. Amer. Stat. Assoc., 1987:705–711):4.6 12.3 7.1 7.0 4.0 9.2 6.7 6.9 11.5 5.111.2 10.5 14.3 8.0 8.8 6.4 5.1 5.6 9.6 7.57.5 6.2 5.8 2.3 3.4 10.4 9.8 6.6 3.7 6.48.3 6.5 7.6 9.3 9.2 7.3 5.0 6.3 13.8 6.25.4 4.8 7.5 6.0 6.9 10.8 7.5 6.6 5.0 3.37.6 3.9 11.9 2.2 15.0 7.2 6.1 15.3 18.9 7.25.4 5.5 4.3 9.0 12.7 11.3 7.4 5.0 3.5 8.28.4 7.3 10.3 11.9 6.0 5.6 9.5 9.3 10.4 9.75.1 6.7 10.2 6.2 8.4 7.0 4.8 5.6 10.5 14.610.8 15.5 7.5 6.4 3.4 5.5 6.6 5.9 15.0 9.67.8 7.0 6.9 4.1 3.6 11.9 3.7 5.7 6.8 11.39.3 9.6 10.4 9.3 6.9 9.8 9.1 10.6 4.5 6.28.3 3.2 4.9 5.0 6.0 8.2 6.3 3.8 6.0
b. What is a typical, or representative, flow rate?
Chapter 9 Solutions
Probability and Statistics for Engineering and the Sciences
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