ESM 206 Problem set 1
1) The Norwegian Lakes dataset on the class website (NorwegianLakes.csv) contains
measurements from 42 lakes, including pH in 1976 and 1981, and estimates of SO4 and
NO3 deposition in 1981. Which variables (if any) appear to be approximately normally
distributed? For those that are not, what transformation might make them more normal?
For each of questions 2-5, (a) state the appropriate null and alternate hypotheses in
words; (b) state which statistical procedure should be used to test the null hypothesis; (c)
run the test; (d) write a short statement giving your conclusion in words and the
supporting statistical information.
2) You are concerned about possible sulfate contamination of groundwater from an
industrial facility. You have data from two wells: one is away from the facility and is
thought to represent background levels in the region; the other is downgradient from the
facility. Here are the data:
Year Month Sulfate concentration (ppm)
Background Downgradient
1995 Jan 560
Apr 530
Jul 570 600
Oct 490 590
1996 Jan 510 590
Apr 550 630
Jul 550 610
Oct 530 630
Test the appropriate hypothesis to decide whether the downgradient site suffers from
sulfate contamination.
3) The file npp.xls on the course website contains data on net primary productivity (NPP)
collected from ecosystems around the world (this is actually a subset of a larger dataset
that can be found in Esser et al. 2000). Test the appropriate hypothesis to decide whether
total NPP (column “TNPP”) differs among ecosystems with different vegetation types
(column “Vegetation type”).
4) A species of marine arthropod lives in seawater that contains calcium in a
concentration of 30 mmole/kg of water. Thirteen of the animals are collected and the
calcium concentrations in their coelomic fluid are found to be: 28, 27, 29, 29, 30, 30, 31,
30, 33, 27, 30, 32, and 31 mmole/kg. Test the appropriate hypothesis to conclude
whether members of this species maintain a coelomic calcium concentration less than that
of their environment.
5) In the Norwegian Lakes data, test the appropriate hypothesis to decide whether the
lakes became more acidic between 1976 and 1981.
