Mathematical Statistics—Homework Assignment #7

Due Friday, March 12 (beginning of class)

Important Reminders

Please respect me, your classmates, and yourself by taking the Honor Code very seriously. Your grade will depend on both the content and exposition of your answers. That is, be sure your logic is clear, you defend all your steps (unless they are, for example, obvious algebra steps), your solutions read smoothly (even if using symbols—they should still read like an English sentences), and that one of your peers could read and understand your solutions without asking any additional questions. In terms of ANOVA analysis, be sure to include all appropriate steps (as we’ve discussed in class) and interpret your results in the context of the problem.

Okay-to-work-together Problems (3 problems)

Chapter 11 Extra Problem

Much of the theory of experimental design grew out of a search for more efficient farming methods (e.g., ways to improve crop yields, ways to raise healthier cows and fatter pigs). It seems natural to think that adding the right vitamins to a pig’s diet might produce fatter pigs faster. In this experiment, the response variable is the weight gain (pounds/week) of the pig. There are two factors: antibiotics (0 mg or 40 mg) and vitamin B12 (0 mg or 5 mg). Hence, there are 4 treatments. Twelve pigs are randomly assigned to the 4 different treatment “diets.” The data are included in the Minitab project Chapter11ExtraProblem.MPJ—in the share folder.

Analyze these data in a mini-report: 1) check the ANOVA conditions (normality and constant-variance) via plots of the residuals (and worded descriptions); if the conditions appear to met then, 2) check if the interaction effect is significant; if the effect is significant, then interpret the results using the interaction plot and your own words—in the context of the problem (and additionally an interpretation of main effects, if appropriate, including pair-wise comparisons); if the interaction effect is not significant, then 3) check if the main effects are significant; if either or both main effect is significant then, 4) use Tukey’s method to see specifically where the significant differences are (and if the results seem practically significant), and 5) write your conclusions in the words/context of the problem.

Chapter 12

32 (in the context of the problem, provide an interpretation of the numerical value of the slope, and also discuss whether the slope is statistically significant)

Work-alone Problems (3 problems)

Chapter 11:

60 (Use Minitab—data file is on the share folder; be sure to use this file, as it’s slightly modified from what’s in the book; Important note: Look graphically and numerically at the data, check conditions (with graphs, numerical summaries, and words), interpret the overall F test, make multiple comparisons, interpret the results in the context/words of the problem, and include all your output—that is, write a mini-report)

Chapter 12