Some Experimental Designs Using Helicopters, Designed by You The following experimental designs were submitted by students in this class. I have selectively chosen designs not because they were good or bad, but because they had strengths and weaknesses, both worthy of comment. We will spend the class time today discussing them together as a class. Your assignment over the weekend will be: choose four of your six designs; get with your group and rewrite what needs to be rewritten on these experimental designs so that they satisfy the criterion below. Please write neatly. As I have said, Mrs. Barrett and I would like to take some of them to Chicago for a national math teachers convention at which we are presenting in three weeks. Next Friday, 7 April, you will conduct two of your four experiments. The criterion by which we (and I) will evaluate the experimental designs you write up is that the answers to the following three questions be yes. 1. If you were given this description of an experiment, would you know everything you needed to know in order to conduct the experiment? 2. Would the appropriate inference procedure for your data be the one that is stated? 3. Is the conclusion that could be drawn from the inference the one that is desired?
Experiment 1: A paired t-test. This experiment will see if there is a difference in the accuracy of two students, Pratik and Erica, trying to hit a target with the same helicopter. The helicopters will be dropped from the third floor of Watts, with both students trying to hit a small target (about 1 foot in diameter) on ground Watts. The distance that the helicopter falls from the target will be measured and recorded for each of the two students. The students will drop the helicopter once in random order each turn (for 20 turns). Who went first each time will also be recorded. The results for each trial will be compared only with one another (not with other trials), hence the use of the paired t-test. The difference in accuracy will not be confounded by the helicopter because both students are using the same helicopter. Experiment 2: A 1-sample proportion. 40 helicopters are dropped from a fixed height. We will test whether more than the claimed 50% of drops hits a target. All helicopters are made with the short-wing design.
Experiment 3: A 1-sample t-test This experiment is designed to detect if the mean distance away from the target for the sample trials of dropped helicopters is equal to the mean distance from the target in the population of trials. Prior to the experiment the group will do a series of 25 trial drops to establish the population mean. One helicopter will be used for the actual experiment. The target will be one foot in diameter. The helicopter will be dropped from 3 rd Floor Watts outside. The distance will be measured from the closest point of the helicopter to the target. The group will use inches as their measuring units. There will be a series of 40 trials to assure the validity of the experiment. This test will be performed at the 5% significance level. The hypothesis test will determine whether the mean distance away from the target for the sample is equal to the mean of the population. (Note: The inference can only be made about the helicopter used. This experiment does not determine whether any difference is due to the person or the helicopter, since these are confounded.) Experiment 4: A 2-sample t-test. Does rotor length affect the speed of the helicopter? Construct two helicopters. One with long rotors and one with short. Have one experimenter drop the helicopters while the other experimenter(s) watch from the ground to see which helicopter lands first. If both were dropped at the same time, the one that lands first would be the fastest. Repeat the test 15-20 times for each helicopter. Drop both helicopters the same number of times to ensure accurate t-procedures. Finally, test the data to see if there is significant evidence that one helicopter falls faster than the other.
Experiment 5: A 1-proportion t-test. This experiment will see if the helicopters can be aimed and hit the chosen target. One person will aim the helicopter at a target and then drop it a total of 20 times. One person will be on ground level and record whether or not the helicopter hit its target or not. Then a hypothesis test will be carried out to see if a helicopter is able to be aimed correctly. Experiment 6: Slope of least squares line 60 helicopters are made and 30 are dropped from one fixed height. 10 of these 30 have a one ounce paper clip, 10 have two paper clips, and 10 have three paper clips. The test is conducted to determine whether there is a positive relationship between weight and time of fall. The null hypothesis is that β = 0. The alternate hypothesis is that β > 0.
Experiment 7: Paired t-test This experiment will determine whether the time it takes 10 helicopters to fall indoors is the same as it takes those 10 helicopters to fall outdoors. The group will make 10 helicopters and drop them from a constant height 20 times, or two times each. Then this will be repeated outside at the same height. The helicopters will be timed and then their times for the trials will be averaged among themselves. For example, Helicopter #1 will be dropped twice indoors, and have the time averaged, then twice outdoors, again having the times averaged. We will then perform a paired t-test to determine whether or not, at the 5% significance level, the times are the same for the helicopters. (Note: the inference can only be made about the helicopter used. This experiment does not determine whether any difference is due to the person or the helicopter, since these are confounded.) Experiment 8: Slope of a least-squares line. We will take several helicopters that are made exactly (we will assume) alike, and weight each one differently. We will then drop each from a set height h, n times, under the same conditions. We will randomize the order they are dropped to try to remove factors of human fatigue on the person dropping or timing. Wwe will collect the times for each weight and then use a least squares line fit to estimate β based on the line s slope b.