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Statistics Experiment: Impact of Sandwiches and Ants or Height and Stepping on Heart Rate, Assignments of Statistics

Two statistics assignments from a university course. The first assignment investigates the effect of different sandwich components (bread, filling, and butter) on the number of meat ants attracted. The second assignment explores the relationship between step height and stepping frequency on the heart rate change of college students. For both assignments, students conducted experiments, collected data, and performed statistical analyses.

Typology: Assignments

Pre 2010

Uploaded on 09/02/2009

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STATISTICS 402 – Assignment 10
Due April 27, 2009
1. What is a picnic without ants? A student in a statistics class in Australia designed
an experiment to see if different types of sandwiches attract different numbers of
meat ants (a scavenger ant found throughout Australia). The results were reported
by Margaret Mackasack (1994), “Favourite Experiments: An Addendum to What
is the Use of Experiments Conducted by Statistics Students?” in the Journal of
Statistics Education, v2n1. The experiment involved different combinations of
bread, filling and butter to make a sandwich. The sandwich was then left next to a
meat ant hill. After 5 minutes the experimenter counted the number of ants within
a specified radius of the sandwich. The factors of interest were; type of bread (rye,
whole meal, multi-grain, or white); the type of filling (Vegemite, Peanut Butter or
Ham and Pickle, and whether butter was put on the bread (yes or no). Two
sandwiches were made for each combination and the order in which sandwiches
were placed near the meat ant hill was completely randomized. Each sandwich
was cleaned up and the ants were allowed to return to the hill before placing
another sandwich. Below are the data.
Filling
Vegemite Peanut Butter Ham and Pickle
Bread Butter Yes No Yes No Yes No
22 18 27 43 68 44
Rye 45 31 50 36 65 54
57 29 42 59 58 34
Whole meal 42 21 36 47 77 65
26 42 60 22 63 36
Multi-grain 28 38 47 19 76 59
52 42 57 24 66 48
White 40 25 51 21 59 53
a. Use the sample size tables from earlier in the semester to determine the size of
the difference in mean quality that can be detected when comparing the:
Two levels of butter.
Three levels of filling.
Four levels of bread.
For all determinations use Alpha=0.05 and Beta=0.10.
b. Construct a complete ANOVA table (you can, and should, use JMP to do the
calculations).
c. What factors and/or interactions are statistically significant at the 1% level?
d. Compute means for those factors that are statistically significant. Indicate
which means are significantly different for the significant factors. Be sure to
include the value of the LSD or HSD used.
e. Compute means for the significant interactions. Construct and interpret
interaction plots for the significant interactions.
f. Based on your analysis, what sandwich attracts the most meat ants? The
fewest meat ants? Support your answer statistically.
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STATISTICS 402 – Assignment 10 Due April 27, 2009

  1. What is a picnic without ants? A student in a statistics class in Australia designed an experiment to see if different types of sandwiches attract different numbers of meat ants (a scavenger ant found throughout Australia). The results were reported by Margaret Mackasack (1994), “Favourite Experiments: An Addendum to What is the Use of Experiments Conducted by Statistics Students?” in the Journal of Statistics Education , v2n1. The experiment involved different combinations of bread, filling and butter to make a sandwich. The sandwich was then left next to a meat ant hill. After 5 minutes the experimenter counted the number of ants within a specified radius of the sandwich. The factors of interest were; type of bread (rye, whole meal, multi-grain, or white); the type of filling (Vegemite, Peanut Butter or Ham and Pickle, and whether butter was put on the bread (yes or no). Two sandwiches were made for each combination and the order in which sandwiches were placed near the meat ant hill was completely randomized. Each sandwich was cleaned up and the ants were allowed to return to the hill before placing another sandwich. Below are the data.

Filling Vegemite Peanut Butter Ham and Pickle Bread Butter Yes No Yes No Yes No 22 18 27 43 68 44 Rye 45 31 50 36 65 54 57 29 42 59 58 34 Whole meal (^42 21 36 47 77 ) 26 42 60 22 63 36 Multi-grain 28 38 47 19 76 59 52 42 57 24 66 48 White 40 25 51 21 59 53

a. Use the sample size tables from earlier in the semester to determine the size of the difference in mean quality that can be detected when comparing the:

  • Two levels of butter.
  • Three levels of filling.
  • Four levels of bread. For all determinations use Alpha=0.05 and Beta=0.10. b. Construct a complete ANOVA table (you can, and should, use JMP to do the calculations). c. What factors and/or interactions are statistically significant at the 1% level? d. Compute means for those factors that are statistically significant. Indicate which means are significantly different for the significant factors. Be sure to include the value of the LSD or HSD used. e. Compute means for the significant interactions. Construct and interpret interaction plots for the significant interactions. f. Based on your analysis, what sandwich attracts the most meat ants? The fewest meat ants? Support your answer statistically.
  1. An experiment is conducted to explore the relationship between height of step (5.75 in or 11.5 in) and rate of stepping (14 steps/min, 21 steps/min or 28 steps/min) on the heart rate of college students. Six college students were used in the study. There are 6 combinations of step height and stepping rate. Each student experienced each combination. The order was randomized for each student and enough time separated the trials so that students’ heart rates could return to a resting rate. The resting heart rate for each student is taken before each trial and the heart rate at the end of the 3 minutes of the stepping regimen is also measured. Below are the data. The values are the change in heart rate from resting to after stepping.

Stepping Frequency 14 steps/min 21 steps/min 28 steps/min Student Step Height 5.75 in 11.5 in 5.75 in 11.5 in 5.75 in 11.5 in 1 16 39 21 52 24 66 2 9 33 21 50 42 60 3 8 18 24 27 27 51 4 9 15 15 28 18 40 5 16 26 28 49 43 59 6 4 15 15 16 20 40

a. Construct a complete ANOVA table for the analysis of the change in heart rate. You can use JMP to do the calculations. b. What, if any, factors and interactions are significant? Support your answers statistically. c. If a factor is significant, what levels are significantly different from other levels? Be sure to include the value of the LSD or HSD used. d. Construct and interpret an appropriate interaction plot. e. Based on your analysis, comment on the effects of step height and rate of stepping on the change in heart rate. f. How important was blocking on the student in this experiment? Support your answer with a statistical argument. This may involve additional analysis. g. If the response had been pulse rate after stepping rather than change in pulse rate, would blocking on student have been more or less important? Explain your reasoning.