1. To examine the effect of diet and mosquito repellent on the amount of mosquito bites, a study was planned. Three people were recruited from each of six counties in Idaho, and the three people in a county were randomized to one of three diets. After a period of time with the diet, each subject had two types of repellent spray randomized to their two forearms. After a few minutes in a mosquito chamber for each arm, an inflammation score was calculated for each arm. The data are contained in this file.
a) Write the linear model for these data, briefly identifying each term
b) Test the null hypothesis for interaction between diet and spray, use a
profile plot to help give a brief statement interpreting your results.
c) Conduct tests of the main effects of diet and spray,
d) Use residual plots to assess the model assumptions.
e) Write a few sentences summarizing your conclusions.
2. A study was planned to compare the taste of five
types of hot dogs: Beef, Chicken, Pork, Tofu, and Turkey. It was decided that
each subject in the study could try only four of the five types of hot dogs. The
following design was proposed to have five subjects each try four hot dogs:
Subject 1 (Chicken, Beef, Pork, Tofu)
Subject 2 (Beef, Turkey, Chicken, Pork)
Subject 3 (Turkey, Chicken, Tofu, Pork)
Subject 4 (Turkey, Pork, Tofu, Beef)
Subject 5 (Tofu, Turkey, Chicken, Beef)
a) What are the values of t, r, k, and b?
b) Solve for the value of lambda.
c) Is the design a balanced incomplete block design? Briefly explain your
answer.
3. Researchers are studying different ways to increase
the vertical jump of basketball players. They recruit 20 players and randomize 4
to each of 5 methods for increasing vertical jump. Each subject is evaluated as
the experiment begins (baseline), and also at 1, 2, 3, and 4 weeks after using
their assigned method.
a) Name this model and write down the model equation.
b) Fill out the 'Source' and 'Degrees of Freedom' columns for the ANOVA table
for this design.
c) Are there possible problems with the standard ANOVA assumptions for these
data? If so, discuss two ways that can be used to analyze these data.