QSCI 482/Prof. Conquest TAs Kennedy, Malinick, Norman
HW 5--DUE FRIDAY, NOVEMBER 8, 2002

1. Recall problem #4 of HW 4 about the effects of Nitrofen on C. dubia
offspring (a one-sample test). The expectation was that Nitrofen would
cause a *decrease* of the average number of offspring to something below
the control value of 32.0. The purpose of this problem is to use the power
calculation from part 4b to fill in the now "blank" power illustration on
page 8-5 of the notes. (You'll need to make a copy of p. 8-5, or just
trace the two curves on a piece of white paper).

On this graph, draw (or shade) in the following: alpha, 1-alpha, beta,
1-beta. (From problem 4b alpha = .10, power = .95.) Label the null
hypothesized value of mu0 = 32. In order to label the value of mu under
the alternative hypothesis (call it muA) for this level of power, you need
to calculate the value of the delta, the minimum detectable effect (MDE),
using the information from #4 in HW4 (n=10, s=3.6). Once you have found
delta, note the relationship between mu0, muA, and delta, and use it to
find muA. Also denote clearly delta, the MDE, on the plot.Finally, the big
vertical line on the graph must be labeled. That line denotes the
"accept/reject" value for xbar. That is, you need to figure out for what
values of xbar would one "accept" Ho, and for what values of xbar would
one reject Ho.

2. Recall the littleneck clam (Protothaca staminea) study done in
Garrison Bay, Washington. Now there are two random samples, each taken
from a different type of sediment. The data are as follows:

Sample from Sediment A: xbar = 40.0 mm, s = 4.6 mm, n =6
Sample from Sediment B: xbar = 40.5 mm, s = 3.5 mm, n=9

a. Test to see whether the two means differ at the .10 level of
significance (you may assume equal variances for this part of the
problem). If they do, compute 90% confidence intervals around the
separate means. If they do not, compute a 90% confidence interval around
the pooled mean.

b. If one wanted to be able to detect a difference between two groups as
small as 0.5 mm, assuming equal sample sizes, what is the minimum n
required to accomplish this? Assume .10 level of significance, power of
.75, and pooled standard deviation of 4.0 mm.

c. Again assuming pooled standard deviation of 4.0 mm, respective
sample sizes of 6 and 9, and a .10 level of significance, what is the
power of detecting a difference between the two group means as low as
1.0 mm?

d. Finally, test to see whether the two variances are indeed equal, at the
.10 level of significance.

3. Below are data concerning Am-241 (Americum-241) concentrations (in
thousandths of pCi/g) in soil crust material collected at two different
locations, one near ("onsite") and one far ("offsite") from a nuclear
reprocessing facility. The purpose of the study is to see whether the
onsite population has larger Am-24a concentrations than the offsite
population.

Population 1 (onsite): 1.74 2.00 1.79 1.81 1.91 2.11 2.00 (n=7)

Population 2 (offsite): 1.45 1.27 1.17 1.01 2.30 1.54 1.71 1.71 trace
(n=9)

NOTE: "trace" means that Am-241 was indeed detected, but in an amount too
small to measure exactly.

At the .10 level of significance, using a test that will incorporate all
the data, including the "trace" measurement, test to see whether Pop. 1
has larger Am-241 concentrations than Pop. 2. What do you conclude?