SOME REVIEW PROBLEMS FOR EXAM 2 [THESE PROBLEMS ARE TAKEN FROM OLD EXAMS].
EXAM 2 IS MONDAY, NOVEMBER 25, 2002. [but finish HW 6 for Friday
first....]
 
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1. Scientists would like to compare fish catch for subsistence
fishers, using two types of hand-thrown nets. Since fishers have
different fishing success according to such factors as location, time of
day, fishing experience, etc., to ensure comparability, each boat fishes
a specified amount of time with one net type, then switches and fishes the
same amount of time with the other net type. The order of net types has
been randomized.
 
 Net Type A Net Type B Difference
 
Boat 1 8.9 7.4 1.5
Boat 2 4.9 3.0 1.9
Boat 3 2.0 2.2 -0.2
Boat 4 5.5 4.4 1.1
Boat 5 9.4 8.7 0.7
Boat 6 6.3 6.9 -0.6
Boat 7 7.4 6.7 0.7
 
MEAN 6.34 5.61 0.73
STD. DEV. 2.54 2.43 0.89
 
a. Use a 95% confidence interval on the mean difference to
decide whether the average catch differs between the two net types.
 
b. If the true average catch difference between the two net types
were equal to 1.0 fish, in doing a two-sided test at the .05 level of
significance, and if we wanted statistical power of 0.75 in order to
detect such a difference, how many boats would we need?
 
c. Now using a *nonparametric* test, test (at the .05 level)
whether the net types have the same catches.
 
2. A small experiment has been done in a lab, where 5 laboratory
dishes have "Type A" culture, and another 5 have "Type B" culture. The
purpose of the experiment is to see whether Type B culture is *more*
conducive to the growth of a particular kind of bacteria than is Type A
culture. At the end of the experiment, the number of separate bacterial
colonies on each lab dish is counted. The data appear as follows:
 
Results from Type A: 0, 0, 0, 0, 4
Results from Type B: 0, 4, 7, 9, 17
 
Because the sample sizes are small, and because the data do not
follow the normal distribution, a nonparametric test is called for
here. At the .05 level of significance, do the test to see whether Type
B culture promotes higher bacterial growth than the Type A culture.
What do you conclude?
 
3. Radio tracking devices were used to record the distances
achieved upstream (km) in Forks Creek, WA, by wild steelhead fish and by
hatchery steelhead fish. Data from the two groups of fish are:
 
wild steelhead xbar = 1.95 s = 3.53 n = 10
hatchery steelhead xbar = 1.33 s = 1.96  n = 8
 
a. Test to see whether the variances of the two steelhead groups are the
same or not (use .05 level of significance).
 
b. Now test the null hypothesis that the two mean distances are equal vs.
the alternative that wild steelhead achieve a *greater* mean distance
upstream than the hatchery fish. (Fishery scientists expect wildfish to
outperform hatchery fish in this respect.) Use the .10 level of
significance for your test; also write down the "P-value" associated with
your test statistic at the end and the tabled value corresponding the the
level of significance.
 
c. Compute a 95% confidence interval for the mean difference in distances
for the two groups and reconcile your result with your answer from (b).
 
d. With sample sizes of 10 and 8, and using a pooled standard deviation of
3.0 km, what would be the minimum detectable distance between the two
population means that we would be able to detect, doing a one-sided test
with a .10 level of significance and statistical power of .75?