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**Unformatted text preview: **Solutions from Montgomery, D. C. (2012) Design and Analysis of Experiments , Wiley, NY 3-1 Chapter 3 Experiments with a Single Factor: The Analysis of Variance Solutions 3.1. An experimenter has conducted a single-factor experiment with four levels of the factor, and each factor level has been replicated six times. The computed value of the F-statistic is F = 3.26. Find bounds on the P-value. Table P-value = 0.025, 0.050 Computer P-value = 0.043 3.2. An experimenter has conducted a single-factor experiment with six levels of the factor, and each factor level has been replicated three times. The computed value of the F-statistic is F = 5.81. Find bounds on the P-value. Table P-value < 0.010 Computer P-value = 0.006 3.3. A computer ANOVA output is shown below. Fill in the blanks. You may give bounds on the P-value. One-way ANOVA Source DF SS MS F P Factor 3 36.15 ? ? ? Error ? ? ? Total 19 196.04 Completed table is: One-way ANOVA Source DF SS MS F P Factor 3 36.15 12.05 1.21 0.3395 Error 16 159.89 9.99 Total 19 196.04 3.4. A computer ANOVA output is shown below. Fill in the blanks. You may give bounds on the P-value. One-way ANOVA Source DF SS MS F P Factor ? ? 246.93 ? ? Error 25 186.53 ? Total 29 1174.24 Solutions from Montgomery, D. C. (2012) Design and Analysis of Experiments , Wiley, NY 3-2 Completed table is: One-way ANOVA Source DF SS MS F P Factor 4 987.71 246.93 33.09 < 0.0001 Error 25 186.53 7.46 Total 29 1174.24 3.5. An article appeared in The Wall Street Journal on Tuesday, April 27, 2010, with the title “Eating Chocolate Is Linked to Depression.” The article reported on a study funded by the National Heart, Lung and Blood Institute (part of the National Institutes of Health) and conducted by the faculty at the University of California, San Diego, and the University of California, Davis. The research was also published in the Archives of Internal Medicine (2010, pp. 699-703). The study examined 931 adults who were not taking antidepressants and did not have known cardiovascular disease or diabetes. The group was about 70% men and the average age of the group was reported to be about 58. The participants were asked about chocolate consumption and then screened for depression using a questionnaire. People who scored less than 16 on the questionnaire are not considered depressed, while those with scores above 16 and less than or equal to 22 are considered possibly depressed, while those with scores above 22 are considered likely to be depressed. The survey found that people who were not depressed ate an average of 8.4 servings of chocolate per month, while those individuals who scored above 22 were likely to be depressed ate the most chocolate, an average of 11.8 servings per month. No differentiation was made between dark and milk chocolate. Other foods were also examined, but no patterned emerged between other foods and depression. ...

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