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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 as coincidences.

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 Carlo method).

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 such simulations.

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 drug.

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?