Statistics 402B
March 31, 2004
Exam 2
Name:
INSTRUCTIONS: Read the questions carefully and completely. Answer the questions and show work in
the space provided. This is the only work that I will look at. Partial 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. Pace yourself, do not spend too much time on any one problem.
Point values for each problem are given.
1. [50 pts] Exposing plant embryos to a growth hormone can promote growth. However, some embryos
exposed to growth hormone become watery and soft and do not grow at all. An experiment is performed
to investigate how the orientation of the embryo (standard or experimental) and the type of medium
the embryos are placed in (Medium 1, Medium 2 or Medium 3) affect how many embryos actually grow.
On a given day, embryos are extracted from white pine seeds and exposed to the growth hormone.
One hundred exposed embryos are then randomly assigned to each of the treatment combinations of
orientation and medium. This process of extracting embryos, exposing them to growth hormone and
randomly assigning embryos to treatment combinations is repeated each day for a total of 10 days.
After two weeks the number of growing embryos for each treatment combination and day of processing
is recorded as %Grow. You can refer to the handout “JMP Output for Analysis of Growth”.
(a) [2] What is the response?
(b) [2] What are the factors of interest?
(c) [2] How many treatment combinations are there?
(d) [2] What are the experimental units?
(e) [5] Why is this a randomized complete block design?
(f) [1] What is the blocking factor?
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(g) [3] For the comparison of orientation level means, how large a difference can be detected? Use
Alpha = 0.05 and Beta = 0.10.
(h) [3] For the comparison of medium level means, how large a difference can be detected? Use Alpha
= 0.05 and Beta = 0.10.
(i) [4] Describe the interaction plot. What does this indicate about interaction?
(j) [4] Is interaction statistically significant? Support your answer with the appropriate F test.
(k) [4] Is there a statistically significant difference between the orientation means? Support your
answer with the appropriate F test.
(l) [4] Are there statistically significant differences among some of the medium means? Support your
answer with the appropriate F test.
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(m) [4] Compute the adjLSD for comparing the means of the three mediums. Choose your confidence
level for an individual comparison so that the overall error rate for set of three comparisons is 0.06.
(n) [5] Compute the F statistic for testing the null hypothesis that all treatment means are equal.
You do not have to complete the test, just give the value of the F ratio.
(o) [5] If the data are analyzed as if they came from a completely randomized design, compute the
F statistic for testing the null hypothesis that the medium effects are zero. You do not have to
complete the test, just give the value of the F ratio.
2. For each of the following scenarios indicate the design used to collect the data. Identify factors of
interest and nuisance factors. Give a partial ANOVA table listing all sources of variation and associated
degrees of freedom.
(a) [7] An experiment is conducted to compare the energy requirements of three physical activities:
running, walking, and bicycle riding. Eight subjects are asked to run, walk and bicycle a measured distance, and the number of kilocalories expended per kilometer is measured for each subject
during each activity. The order of the activities is randomized for each individual with time for
recovery between activities.
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(b) [8] An experiment is designed to determine which of four movies has the greatest appeal. The
four movies are: A: Action, B: Science Fiction, C: Comedy and D: Drama. Only one theater is
available for one week for the experiment. The time of day and day of the week a movie is shown
may have an effect on a movie’s appeal. Therefore, we want to account for time of day and day
of week variation in our analysis. Each movie is shown once on each day of the week (Monday,
Tuesday, Wednesday and Thursday) and once at each time (matinee, early evening, mid evening,
and late evening). Each movie is shown to 50 volunteers and the number of volunteers who would
recommend the movie to a friend is recorded.
3. [10 pts] Advantages and disadvantages of block designs.
(a) [6] What is the principle advantage of a randomized complete block design over a completely
randomized design.
(b) [4] Give two disadvantages of a randomized complete block design.
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