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,
α
= 0.05,
α
= 0.01, and
α
= 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.
Using the data from the previous question, test the null hypothesis that the mean
dissolving time is no
less
than 45 seconds.