PUT YOUR NAME ON EVERY PAGE OF YOUR ANSWERS. YOU MAY USE
THE BACKS OF
PAGES. BUT!--KEEP THE PROBLEMS
*SEPARATE*, SINCE THE EXAM WILL BE
SEPARATED FOR GRADING PURPOSES.
NOTE: WHEN DOING
ANY HYPOTHESIS TESTING, YOUR CONCLUSION SHOULD BE *MORE
THAN* SIMPLY WORDS LIKE "ACCEPT
Ho" OR "REJECT Ho". YOU SHOULD HAVE A
SENTENCE OR TWO THAT RELATES THE CONCLUSION OF THE
STATISTICAL TEXT BACK
TO THE ORIGINAL CONTEXT OF THE PROBLEM.
IT IS *NOT* NECESSARY TO
WRITE DOWN ALL THE ASSUMPTIONS THAT GO ALONG WITH EACH
TEST. THERE ARE 4
SEPARATE QUESTIONS. EACH QUESTION HAS SEVERAL PARTS.
1. In a breeding locale, both
campus) and white geese exist.
The
population; white geese
constitute 40%. A survey of "next generation chick
broods" was conducted. The
survey noted whether the chicks were a result
of two
parent is a Canada goose and one
parent is a white goose). The
investigators are interested in
whether the mating among members of the
two populations is essentially
random, or whether some other phenomenon is
operating.
The actual data are as follows:
CANADA-CANADA BROODS 641
WHITE-WHITE BROODS 130
CANADA-WHITE BROODS
29
a. [09 pts.] Out of a total of 800 broods, write
down the expected
number of broods that are:
CANADA-CANADA
WHITE-WHITE
CANADA-WHITE
b. [15 pts.] Doing a test at the
.05 level of significance, calculate the
test statistic and come to the
appropriate conclusion regarding whether
the hypothesis of random mating
holds for these data. What do you
conclude?
c. [02 pts.] Which category is
responsible for the largest contribution to
the value of your test
statistic?
d. [04 pts.] From data
inspection (NO further testing here!), what seems
to be going on with these data?
2. Scientists from the
Planning and Design studied the relationship between
counts of flash
flooding during certain types of
storm events, and intensity of
urbanization. Four categories of intensity of urbanization
were noted,
with counts of flash flood
events recorded.
Intensity of Urbanization: A B C D
No. of flash flood events 20 18 33 19
a. [24 pts] The categories
pertain to intensity of urbanization; they are
roughly equally spaced, and they
are as follows: A is "No
Urbanization",
B is "Low Amount of Urbanization", C is "Moderate Amount of Urbanization",
D is "Intense Urbanization". Using the most powerful available test, test
the null hypothesis of
uniformity with respect to the distribution of
flash flood events over the 4
categories of urbanization using the .05
level of significance. What do you conclude?
b. [04 pts] By data inspection
(*no* further testing here!), what seems
to be the relationship between
intensity of urbanization and the presence
of flash flood events?
3. Scientist assigned a group of homogeneous volunteers
[i.e., all the same
sex, bodymass,
and general fitness] randomly to each of four treatment
groups (A, B, C, D).
Each individual was exposed to a virus well-known for
causing common warts, and after a specified period of time it was noted whether
each individual had
experienced common warts, or
not. Results are as follows:
A B C D
WARTS 21 08 02 10
NO WARTS 05 17 24 17
TOTAL 26 25 26 27
a. [08 pts.] Assuming
that the null hypothesis of "homogeneity among the treatments" is
TRUE, compute the best estimate of probability of experiencing warts for the
Treatment C group.
b. [05 pts.] Assuming that the
null hypothesis of "homogeneity among the treatments" is true,
compute the EXPECTED COUNT for the "No Warts, Treatment B" group.
c. [05 pts.] The computed test
statistic to test the null hypothesis
[stated above] comes out to be
30.21. At the .05 level of significance,
what is the appropriate
conclusion? Include the critical tabled value to
do the test.
d. [02 pts.] Find the two
treatment groups that look *most like
each other* [this would be
"Step 1 in a subdivision process".]
e. [10 pts.] Do the subtest for
*only* the two treatment groups from part
[d].
4. A statewide
Washington Standards for Learning (WASL) test is designed to have a normal
distribution of resulting scores, with a population a mean score of mu=250 and a standard deviation of sigma=50.
a. [05 pts] For an individual
drawn at random from the population, what is
the probability of an
individual's score being greater than 205?
b. [06 pts] What two values
capture the middle 54% of the population?
c. [05 pts] 91% of the population will have a score
greater than what value?
d. [07 pts] If 25 individuals are drawn at random from
this population,
what is the probability that
their average score will be greater than 245?
e. [07 pts] If 25 individuals are drawn at random from
this population,
65% of the time their average score will be between what
two values?