Tesitng: T-Test Example
| Example: Eyespot
Many accounts suggest that many species of animals
find direct stares from another animal aversive.
Some moths have developed eye-spot patterns on their
wings or bodys to ward off predators. An experiment
was done using 16 moth-eating birds. These birds
were tested in a two-chambered box that they were
free to roam in from side to side. One chamber had
two eye-spot patterns painted on the wall. The other
chamber had plain walls. Each bird was left in the
chamber for 60 minutes, and the amount of time spent
in the plain chamber was recorded.
Here are the four steps involved in the statistical
- State the Hypotheses: The null hypothesis
is that there is no effect for eye-spots painted
on the wall. Birds should spend half their time
-- 30 minutes -- in each room. The alternative
hypothesis is that there is an effect. In symbols
the null and alternative hypotheses are:
- Set the decision criteria: We arbitrarily
decide on an alpha level
We also note that there are 15 degrees of freedom:
The table tells us that the critical region consists
of t values less than -2.131 and greater than
- Gather Data:
The mean is 35 minutes in the plain side, and
the sample variance is 81.
- Evaluate Null Hypothesis:
The formula for the estimated standard error is:
For these data, the estimated standard error is
Sqrt(81/16) = 2.25
The formulat for T is:
Thus, for these data, T = (35-30)/2.25 = 2.22
Since 2.22 is in the critical region, we reject
the null hypothesis that the presence of eye-spot
patterns does not influence behavior.
Report for the Eyespots Data.
- Two more ViSta examples
- Z-Test: In-class survey SAT Math and Verbal data (pop
mean=460, pop stdv=100). ViSta
| Report for the SAT Verbal Variable
| Report for the SAT Math Variable
- T-Test: Newcomb Lightspeed
These data are from the first experiment to determine
the speed of light. The best modern measurements correspond
to a passage time of 33.02 in this experiment. The population
standard deviation is unknown.
| Report for the Newcomb Lightspeed Data