QSCI 482, Fall 2002 REVIEW QUESTIONS FOR EXAM 1
Answers will be made available on the class webpage
http://faculty.washington.edu/conquest

1. Scientists have noticed that in certain tropical locations, muddying of
the waters from soil erosion is so bad that certain species of colorful
fish are having difficulty distinguishing between mates of their
particular species and mates of other species, so mating may essentially
occur "at random" in terms of which species a fish mates with. Suppose
that 28 percent of the fish are of species A and that the remaining 72
percent are of species B. 52 matings have been observed, as follows:

TYPE OF MATING AA BB AB
NUMBER 12 34 06

a. Write out the expected counts for the number of: A-A matings, B-B
matings, and A-B matings under the null hypothesis of random mating.

b. Calculate the residual for any ONE of the three
categories and interpret its value.

c. If we are testing the null hypothesis of random mating at the
alpha=.05 level of significance, and the value of the observed test
statistic is 27.9, what is the appropriate conclusion? Write down BOTH the
appropriate tabled critical value and the P-value associated with your
test statistic.

d. From data inspection of observed and expected values (no further
calculations necessary!), what seems to be going on?

2. Fruit flies are counted in the wild by putting out traps
with yeast cultures (to lure the flies in with food). Five different
types of yeast cultures, with different amounts of "Agent X"
were used to investigate whether the different yeast cultures perform
similarly as bait for fruit flies, or whether "Agent X" actually
makes a difference as a lure. We do not know the exact amount of
Agent X in each of the cultures; we do know that we may consider
the categories as being roughly equally spaced.

Level of Agent X: None Low Moderate Higher Highest

No. of flies caught: 42 28 15 12 03

a. Test the null hypothesis that the level of Attractant X has
no effect upon the number of flies caught in the five yeast cultures.
(Level of significance = 0.05.) Use the most powerful test available,
the one that is most likely to reject the null hypothesis when it is
in fact false. What is your conclusion?

b. By data inspection (no further testing here), what seems to be
the relationship between the level of Agent X and the number of flies
caught?

3. Scientists in an Arctic expedition measured the thermal dependence of
3acterial enzyme rates in 4 different environments: permanent sea-ice, new
sea ice, water-column, and sediment trap. Enzymes were classified as
"Psychrophile" if the enzyme maximal activity occurred below 15 degrees;
or "Psychrotolerant" is the enzyme maximal activity occurred above 15
degrees.

Environment Result:
Psychrophile Psychrotolerant Total samples
_____________________________________________________________________

Permanent sea-ice 3 1 4
1st year sea-ice 3 12 15
Water column 3 10 13
Sediment trap 10 14 24

Totals: 19 37 56

a. From the description above, write down the appropriate null
hypothesis (in specific statistical terms) that corresponds to "no
difference among environments in terms of the distribution of maximal
enzyme activity".

b. If the null hypothesis is true, fill in the expected counts
any 2 of 4 environments for the "Psychrophile" category.

c. If the value of the observed test statistic is 5.63, state
the statistical outcome AND the associated P-value that goes along with
the observed test statistic.

d. Write down the appropriate biological interpretation from
the results of the statistical test.

4. A normally distributed population of sardine lengths processed by
Ocean Beauty Seafoods has a mean length of 4.54 inches with a standard
deviation of 0.25 inches.

a. What proportion of the sardines will be greater than 4.1 inches?

b. What is the probability that a sardine drawn at random from this
population will have a length less than 4.3 inches?

c. 90% of the sardines will have a length less than what value?

d. What values capture the middle 95% of the population?

e. If 50 sardines are drawn at random from this population, what is the
probability that their *average length* will be less than 4.50 inches?

f. If we wanted to ensure that the standard error of the mean (Zar,
Section 6.3) for a random sample drawn from this population, was no
greater than 5% of the population mean, how large a random sample would
we have to take?