Environmental Data Analysis EESC
BC 3017
Homework 6 - due Th 11/5
Significance tests
1.) (8p) Your employee has
performed a job for you and
estimates the cost to be $7320. You doubt this estimate and decide to
perform
a hypothesis test. From a list of actual costs of jobs similar to the
job
your employee estimated, you randomly select 49 to test the estimate.
The
mean and standard deviation of the sample are $7500 and $700,
respectively.
Again, formulate null and alternate hypotheses. Is the difference of
$180
significant at the 95% level?
2.) (8p) In order to determine if students make a systematic
error
when counting particles on a scotch tape, artificial samples were
prepared
by putting exactely 70 large particles on each of 6 1cm2
large pieces of scotch tape. The student counted the following 6
results:
72, 79, 65, 84, 67, 77. Does the student introduce a systematic error
into
the measurement?
(a) perform the test using a confidence interval
(b) Formulate the null and alternate hypotheses and perform
a t-test at the 95% significance level.
3.)
(8p) Ttest on cell experiments. Chemical
compounds that are
carcinogenic to mammals also commonly cause genetic mutations in lower
organisms. Preliminary screening of possible cancer-producing compounds
can be performed by testing whether these compounds increase the
mutation
rate of microorganisms. Comparison of the log transformed colony counts
of the untreated and treated groups can provide evidence for the safety
of the chemical. (The logarithm of the colony count is used here
instead
of the count itself, because the data are heavily skewed. So, "2"
stands
for 102 colonies = 100 colonies).
Perform a ttest on the log colony counts as given in the table below
to find out if there is sufficient evidence for the hypothesis that the
particular chemical tested affects cell numbers/mutations.
| Control |
Treatment
|
|
2.13
|
1.42
|
|
1.59
|
1.73
|
|
1.14
|
1.57
|
|
1.77
|
1.49
|
|
1.36
|
2.52
|
|
1.46
|
1.83
|
|
1.19
|
1.35
|
| |
1.53
|
Regression analysis
4) (8p) New York City
has seen a considerable drop in crime rate
in the last decades. Unemployment has been quoted as one potential
factor controlling crime. Download this excel file that shows the
motor vehicle theft rate (=total number of thefts per 1000 NYC
Population) and the unemplyment rate in % for NYC. Plot both varaibles
as a function of time, make a scatter plot, perform a statistical
analysis, and answer the question: Is motor vehicle theft rate
correlated with unemployment rate?