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Introduction: This is a two day unit plan that incorporates
some decision-making ideas from statistics into the science classroom.
It is intended for intermediate level science students (about
high school freshman age) and beyond. No previous experience
with statistical analysis is required. The NCTM Statistics Standard
is taken into account in this lesson by having students make use
of sampling to back up a claim and by having students design (with
teacher assistance) a statistical experiment to study a problem.
Acid Rain Lab: Acid rain is literally acid in rain water.
It is a weak acid (sulfuric and nitric) but strong enough to
damage buildings and statues and harm lakes, forests, and crops.
The purpose of this lab is to investigate the damaging effects
of acid rain on plants. In particular, students will determine
whether and/or to what extent acid rain affects the germination
rate of turnip seeds. The germination rates of seeds placed in
an acid rain solution will be compared with that of the control--seeds
placed in distilled water. Statistical methods will then be employed
to determine whether any differences in germination rates is attributable
to the acid rain or if it is reasonable to explain any differences
The acid rain solution should be a mixture of dilute sulfuric
and nitric acids (about pH 4). Students, working in groups of
no more than four, should sandwich exactly 25 turnip seeds (or
some other type of seed) between two layers of paper toweling
saturated in acid rain solution. (There should be no pools of
solution.) Each group should also prepare a control Petri dish
in which distilled water is used in place of the acid rain solution.
The Petri dishes should then be wrapped in aluminum foil to keep
them in darkness and allowed to remain undisturbed (preferably
for a weekend).
After allowing the seeds time to germinate, the students should
count the number of seeds that germinated in each and calculate
germination percentages. The students will most likely find that
fewer seeds germinate in the experimental Petri dish than in the
control. However, this does not necessarily mean that acid rain
was to blame. If the percentages were not too far apart (say
90% for the control and 72% for the experimental), it is conceivable
that the difference may just be coincidence, the result of random
chance. The 90% rate for the control suggests that about 10%
of the seeds donít germinate even in ideal conditions.
That is, 1 in 10 seeds were just ìduds.î Is it
not possible to pick 25 seeds from a bag, of which 1 in 10 is
destined not to germinate, and get 8 of those duds (amounting
to a 68% germination rate)? It may not be very likely, but it
is possible. In order to be confident that the acid rain and
not coincidence is responsible for the results, it is desirable
to know just how likely it is to have gotten only a 68% germination
rate if any given seed has a 90% probability of germinating.
This can be accomplished by doing many, many actual trials (lots
of Petri dishes), or, more realistically, by simulation (the Monte
Personal Classroom Experience: The following is a description
of the ìacid rain labî that I did with my intermediate
physical science students (mostly high school Freshmen). I have
five classes and did the lab in each class. We pooled our results
for the control and averaged about an 80% germination rate. From
this we determined that under ideal conditions--or, as ideal as
we could make them in our lab--that any given turnip seed in our
supply has about an 8 in 10 chance of germinating. Each group
then had the task of determining whether or not the results of
their experiment could be explained by chance. A typical experimental
germination rate for my students was 60%. We used random number
tables to simulate many experiments. We assumed that the acid
rain had no affect in our analysis. Most groups chose to use
the following model: digits 0-7 correspond to a seed germinating
and digits 8 and 9 correspond to a seed failing to germinate.
A trial consisted of a row of 25 random numbers, one for each
seed. The outcome of the trial is determined by counting the
number of digits between 0 and 7, inclusive, and computing the
percentage of successful germinations. This percentage is recorded
along side the trial. This is repeated until 30 trials are done.
Below is typical set of simulated trials that I created using
a spreadsheet rather than a random number table hard copy. (If
your class has access to a spreadsheet program such as Excel 5.0,
I highly recommend using it. The tedious tasks of counting successes
and computing percentages is eliminated thanks to the COUNTIF
function. On the other hand, if you have students in your class
who still could use practice computing percentages--as I do--then
you may wish to hand out copies of random number tables.)
Notice that in only one of the 30 simulated trials did a set of
seeds do as ìpoorlyî as the experimental seeds.
That is, only about 3% of the time did a simulated Petri dish
have a 60% germination rate or less. My students were able to
conclude with confidence, then, that our assumption about acid
rain having no effect was wrong, since seeds doing as poorly as
their in ideal conditions is rare, happening only 3% of the time.
Acid rain, therefore, does have a negative impact on the germination
rates of turnip seeds.
In my classes, the experimental germination percentage varied,
and one group actually did find that their germination rate would
happen by chance around 17% of the time. This was not unlikely
enough to say for sure that the acid rain and not pure chance
was responsible for the poor performance of their seeds when compared
to the control.
Our time schedule: We prepared our experimental and control
Petri dishes the day before a long weekend. This took about half
the period. It should be sufficient, however, to give the seeds
from a Friday to a Monday to germinate. Upon returning to school,
we spent half a period collecting data. The next day we spent
the entire period doing the statistical analysis. It took the
entire period because this was my studentsí first exposure
Comments: The most difficult part of the experiment for
my students was in interpreting the results of their statistical
analyses. They often got confused by their results and werenít
sure whether the results implied that acid rain was certainly
the culprit or that it was undoubtedly due to coincidence. My
recommendation is that you explain to the class as a whole how
to interpret the results and question groups individually to see
if they understand their particular results. This explanation
may require at least half a period if the mathematics ability
of your student is not very high.
Here are some questions to accompany your normal lab questions.
1. Just by comparing the germination rate in your Petri dish
with that of the control, what would you conclude about acid rainís
effect? Does your conclusion become more or less convincing after
having done your statistical analysis? Why?
2. Is it possible for only 2 out of 10 seeds to be ìdudsî
and when reaching in to pick out 25 seeds at random, you end up
with all 25 of them being duds?
3. If you had done more than 30 trials and gotten the same results
(that is, found that the same percentage did as badly or worse
than in your Petri dish), would you feel more or less confident
about your conclusion? Explain why.
4. What implications do the statistical concepts encountered
in this lab have for the medical profession? Hint: Think
about an experiment designed to test the effectiveness of a new
5. How would you have to change your statistical experiment if
you had used 30 rather than 25 seeds and the control germination
rate had been 5 out of 6 rather than 8 out of 10?