ESM 206 Problem Set 1
MicroExam due Friday, December 7
For the short version, I recommend trying at least A1, 5, 6, 7, 9; in section B, doing the
power analysis for at least one of each type of t-test; doing all problems in sections C, E,
and F; and in section D, assessing normality for problems 1 and 9.
A:
t
-test practice
For each of the following questions, (a) state the appropriate null and alternate
hypotheses; (b) state which statistical procedure should be used to test the null
hypothesis; (c) run the test, reporting the values of
t
, degrees of freedom, and
P
; (d) draw
conclusions based on
α
= 0.1,
= 0.05,
= 0.01, and
= 0.001.
1.
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.
2.
Twenty-five intertidal crabs were placed in air at 24.3
°
C, and their body
temperatures were measured as: 25.8, 24.6, 26.1, 22.9, 25.1, 27.3, 24.0, 24.5,
23.9, 26.2, 24.3, 24.6, 23.3, 25.5, 28.1, 24.8, 23.5, 26.3, 25.4, 25.5, 23.9, 27.0,
24.8, 22.9, 25.4. Test the appropriate hypothesis to conclude whether members of
this species maintain their bodies at a different temperature than the air.
3.
The menstrual cycles in a random sample of fifteen women, measured in days,
were found to be: 26, 24, 29, 33, 25, 26, 23, 30, 31, 30, 28, 27, 29, 28.
Test the
appropriate hypothesis to determine whether the average human menstrual cycle
equals a lunar month (29.5 days).
4.
Over eight repeated experiments, the dissolving time (in seconds) of a drug in
gastric juices was found to be: 42.7, 43.4, 44.6, 45.1, 45.6, 45.9, 46.8, 47.6.
Test
the null hypothesis that the mean dissolving time is no more than 45 seconds.
5.