Stat 402 B – Exam 2 Take-home Problem
Due in class Friday, April 3, 2015
1. [35 pts] You are asked to help design an experiment involving the effect of exam aids on the
performance of students on the first exam in an introductory statistics course. The treatments
are:
1. No calculator and no formula sheet
2. No calculator and text formula sheet
3. No calculator and instructor made formula sheet
4. Simple calculator and no formula sheet
5. Simple calculator and text formula sheet
6. Simple calculator and instructor made formula sheet
7. Graphing calculator and no formula sheet
8. Graphing calculator and text formula sheet
9. Graphing calculator and instructor made formula sheet
Ninety students in an introductory statistics course, all of whom took a mathematics
placement test, have agreed to participate in the experiment. The response variable is the
score on the first exam.
a) [4] The treatments can be thought of arising from factorial crossing of two factors. What
are those two factors? Be sure to give the levels of each of the factors you identify.
b) [2] What are the experimental units?
c) [2] Give an outside variable that should be controlled. Indicate how you would control
the variable that you identify.
d) [8] Describe how you would conduct a completely randomized experiment to examine
the two factors and their interaction.
i. What is the size of the difference in treatment means that can be detected with Alpha
= 0.10 and Beta = 0.10?
ii. What is the size of the difference in factor level means that can be detected with
Alpha = 0.10 and Beta = 0.10?
iii. Explain in detail how you would randomize. Include a randomized assignment of
experimental units to treatments.
iv. Give a partial ANOVA table listing all sources of variation and the associated
degrees of freedom.
e) [2] For this completely randomized experiment, what contributes to random error
variation?
f) [3] Explain briefly why a completely randomized design may not be the best design given
the purpose of the experiment.
g) [9] Describe how you would conduct a randomized complete block experiment.
i. Indicate how you would form blocks. Be specific about what you will do to form
blocks and how many blocks you will have.
ii. Explain in detail how you would randomize. Include a complete randomized
assignment of treatments.
iii. Give a partial ANOVA table listing all sources of variation and the associated
degrees of freedom.
h) [2] For this randomized complete block experiment what is the smallest difference in
treatment level means that you will be able to detect with Alpha = 0.05 and Beta = 0.05?
i) [3] For this randomized complete block experiment what contributes to random error
variation?