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 Canada geese (the kind that populate the UW

campus) and white geese exist. The Canada geese constitute 60% of 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 Canada geese mating, or two white geese mating, or a "mix" (one

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 University of Washington's Department of Urban

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?