QSCI 482/Prof. Conquest TAs Kennedy, Malinick, Norman

HOMEWORK 4 - DUE FRIDAY, NOVEMBER 1, 2002

1. The following data set is a sample of the corvina fish catch
(Sciaenideae) in the "primera" catch category, in kg/boat, from the
Gulf of Nicoya in Costa Rica. It has been speculated that the data
from the nonzero catches are lognormally distributed; that is, the
natural logarithms of the catches follow a normal distribution.
Here are the original data (in kg/boat-trip):

28.7, 145.2, 18.0, 28.2, 7.9, 11.2, 7.4, 3.8, 26.9, 11.4, 6.6, 100.0,
17.8, 2.5, 5.8

a. Using SPSS [or your favorite statistical software], do [1] a
histogram of the data and [2] a normal probability plot of the data.
Examine the histogram for symmetry and "bell-shape" and any extreme
values; examine the normal probablity plot for normality. Give a brief
description of what each plot seems to show.

b. Repeat the above (histogram and normal probability plot) on the natural
logarithms of the data. What do you conclude about the characteristics of
the data (catch vs. log catch), by looking at the graphs?

2. Ocean Beauty Seafoods is purchasing new batches of sardines from a
different supplier. Their inspectors are not sure whether the average
length of the sardines from this supplier are the same as or different
from the "old standard" of 4.54 inches. A random sample of n=100 sardines
is drawn from the population, giving a sample mean length of xbar=4.51
inches and a sample standard deviation of s=.23 inches. (You may assume
that sardine lengths follow a normal distribution.)

a. At the .05 level of significance, test to see whether the mean length
of the new batches is different from the "old standard" of 4.54 inches.
Include the P-value with your statistical results. What do you conclude?

b. Compute a 95% confidence interval for the population mean sardine
length of the new batches. Reconcile the result that you get for your
confidence interval with your answer to part (a) above.

3. A study of littleneck clams (Protothaca staminea) was done in Garrison
Bay, Washington. The following data on variability in shell width was
collected from a random sample of 16 clams:

std. deviation s = 4.6 mm
n = 16 clams

a. Compute a 95% confidence interval for the standard deviation of the
population.

PROBLEMS 3b, 4b BELOW ARE BASED ON TOPIC 8 [so you might wish to wait
until after Monday's class before attempting them].

3b. For the littleneck clam data, how large a sample is needed to reject
Ho: mu = 40.0 mm vs. Ha: mu not equal to 40.0 mm if in fact the *true
population mean* mu is really 38 mm? (Use s=4.6 mm, alpha = .10 for
variety, beta = .10.)

4. Scientists have conducted studies on the reproductive toxicity effects
of Nitrofen, an herbicide used for weed control in rice and other grains.
Nitrofen is persistent in aquatic systems. Its reproductive toxicity
effects were tested on Cladocera dubia (a zooplankton) at a certain
concentration.

a. Suppose we want to compare these data to a *documented standard control
value* of mu=32.0. Even before running the experiment, enough has been
known about Nitrofen to suspect that if Nitrofen does anything at all to
C. dubia, it should *decrease* the average number of offspring.

Assuming normality of the data (or at least regarding the behavior of
the sample mean), do a test at the alpha = .10 level to see if there has
been a decrease in the average number of offspring when compared with the
standard control value of 32.0. Be sure to write down the null and
alternative hypotheses. Include the P-value associated with your test
statistic.

The data for this part (3a) are as follows: for each of 10 animals, the
number of offspring was recorded, yielding a sample average of 28.3
offspring and a sample standard deviation of s=3.6 offspring.
What do you conclude as a result of your test?

b. If we want to achieve 95% power to test the null and alternative
hypotheses as in part (3a) above, what kind of minimum detectable effect
would we be able to detect statistically? Use alpha = .10, n=10, and use
3.6 as the standard deviation.