Statistics 402B
April 8, 2011
Exam 2
Name: __________________________
INSTRUCTIONS: Read the questions carefully and completely. Answer the questions
and show work in the space provided. Give appropriate units with all summary values.
Credit will not be given if work is not shown. Be sure to answer all questions within the
context of the problem. Refer to the computer printout and graphs provided when
appropriate. If the computer printout has the answer use it, you do not have to do a hand
calculation if it is already done for you by the computer. Pace yourself. Do not spend
too much time on any one problem. Point values for each problem are given.
1. [25 pts] The text discusses an experiment to compare the effect of four different doses
of insulin (A, B, C, and D) on the blood glucose level of rabbits. The blood glucose
level (mg/dL) is measured 50 minutes after the injection with insulin.
a. [1] What is the response?
b. [1] What are the conditions?
c. [1] What are the experimental units?
d. [2] If we were going to conduct the experiment using a completely randomized
design, how many rabbits would you need to detect a difference in dose means of
1.6 standard deviations with Alpha = Beta = 0.05?
e. [4] Give two reasons why conducting the experiment as a block design (forming
blocks by reusing rabbits) is better than a completely randomized design.
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f. [4] Reusing rabbits creates a problem because it takes a day for the insulin dose to
wear off before the next dose can be administered. Explain what the problem is
and how a Latin Square design takes care of this problem.
g. [3] A Latin Square experiment with rabbit and day as the two nuisance factors
was randomized and run. Below are the dose sample means. Compute the
estimated effect of each dose and indicate which dose(s) has(have) the biggest
effect on blood sugar level.
Dose
Mean
Blood
Glucose Level
A
B
C
D
56.0 mg/dL
40.0 mg/dL
53.0 mg/dL
35.0 mg/dL
Estimated
Effect
Below is the ANOVA table for the analysis of the blood sugar level data.
Source
Model
Doses
Day
Rabbit
Error
C. Total
df
9
3
3
3
6
15
Sum of Squares
2136.0
1224.0
504.0
408.0
214.0
2350.0
Mean Square
237.333
408.0
168.0
136.0
35.667
F – Ratio
6.654
11.439
4.710
3.813
Prob > F
0.0158
0.0068
0.0767
0.0510
h. [4] Test the hypothesis that the dose effects are zero against the alternative that
some dose effects are not zero.
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i. [5] The value of the Tukey-Kramer HSD is 14.62. If you wanted to get the lowest
blood sugar value, which dose would you recommend? Support your answer
statistically.
2.
[25 pts] 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 change of heart rate of college students. Six college students are
used in the study. There are 6 combinations of step height and stepping rate. Each
student experiences each combination. The order is randomized for each student and
enough time separates the trials so that students’ heart rates 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 3 minutes of the stepping combination is also measured. The change in
heart rate is calculated by subtracting the resting heart rate from the heart rate after
stepping. Refer to the JMP output for the “Stepping Experiment.” Note: There are
several different analyses of the data in the JMP output, not all of which are correct.
a) [4] What are the response, conditions of interest and experimental material?
b) [4] What design was used to collect the data? Explain how you know what design
was used.
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c) [3] Are there statistically significant differences among the sample means for the
step heights? Report the appropriate F-statistic, P-value, decision, reason for the
decision and conclusion.
d) [3] Are there statistically significant differences among the sample means for the
stepping frequencies? Report the appropriate F-statistic, P-value, decision, reason
for the decision and conclusion.
e) [4] Comment on the interaction plot. Describe what you see in the plot and what
it indicates about the possible interaction between step height and stepping
frequency.
f) [3] For comparing treatment (combination of height and frequency) means the
value of q is 3.08179. Compute the value of HSD.
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g) [4] What would your recommendation be if you wanted the largest average
increase in heart rate? Support your answer statistically.
3. [20 pts] Name that design! For each of the following scenarios indicate what design
is used. Indicate the response variable, factors of interest, whether factorial crossing
is used to make treatments, nuisance factors and provide a partial ANOVA table
listing all sources of variation and associated degrees of freedom.
a. [7] A marketing firm sets up an experiment to see if coupons or mail-in rebates
have an effect on unit sales of a product. In each store, there is a display with the
product. The treatment combinations are: (1) no coupon and no rebate, (2) $1
coupon and no rebate, (3) no coupon and $1 rebate, (4) $1 coupon and $1 rebate.
The marketing firm selects 10 stores at random. Each store will display the
product under each of the treatment combinations for one week and record the
unit sales. The order of the treatment conditions will be randomly assigned at
each store.
Design:
Source
df
Factors:
Is factorial crossing used?
Nuisance variables:
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b. [6] An experiment (field trial) is conducted to investigate the yield of corn using 5
different levels of nitrogen fertilizer. There is one variety of corn used throughout
the experiment. The five levels of nitrogen are: 0 lbs/acre, 30 lbs/acre, 60
lbs/acre, 90 lbs/acre and 120 lbs/acre. To get a better picture of yield across the
state, there are five locations that will be used in the experiment. At each
location, there are five plots. Five plots are selected from the 25 plots (five plots
at five locations) at random and assigned 0 lbs/acre. Five plots are selected from
the remaining 20 plots at random and assigned 30 lbs/acre. Five plots are selected
from the remaining 15 plots at random and assigned 60 lbs/acre. Five plots are
selected from the remaining 10 plots at random and assigned 90 lbs/acre. The
remaining five plots are assigned 120 lbs/acre.
Design:
Source
df
Factors:
Is factorial crossing used?
Nuisance variables:
c. [7] An experiment is conducted to see the effect of brand of golf ball and brand of
driver on the length a golf ball travels. There are three brands of golf ball:
Calloway, Nike and Titleist. There are two brands of driver: TaylorMade and
Cleveland Golf. Because driving skill and strength may vary from one golfer to
the next, six different golfers will be used in the experiment. Because weather
conditions vary from day to day the experiment will be run over six days. Each
golfer will do five drives with a combination of golf ball and driver on each day.
The lengths of the five drives will be averaged to give one value. Each
combination of ball and driver is used once on each day and once by each golfer.
Design:
Source
df
Factors:
Is factorial crossing used?
Nuisance variables:
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