Materials and Environment
The materials used to conduct this experiment include: 1 pair of scissors, three paper clips, and 15 sheets of 8.5x11’’ .01lb printable paper, a ruler, and a stopwatch.
The experiment was conducted in classroom 123 of the McNair engineering building.
Methods
The proposed null hypothesis (H0 ) was there would not be a difference between the three means; the proposed alternative hypothesis (Ha ) was that at least one of the means would differ. The independent variable was the paper clips; the dependent variable was the flight time. The steps for the experiment were as followed:
- One person cut out and folded 15 paper helicopters according to the dimensions of the original design.
- The 15 paper helicopters and 3 paper clips were randomly placed on the table.
- Another person randomly selected a paper helicopter and a paper clip.
- The paper clip was placed on the tail end of the paper helicopter.
- The paper helicopter was then dropped at a height of 6’.
- The flight time was then recorded.
- Steps 3-6 were repeated until a total of three paper clips were added to the tail end of the paper helicopter.
- Steps 3-7 were repeated until all the remaining helicopters were tested.
To ensure the experiment exhibited replication, one member was responsible for cutting out all 15 of the helicopters, the same type of paper was used for all 15 helicopters, a different paper helicopter was used for each drop, and the helicopter was dropped by the same member at the same height each time. To assure that each helicopter was dropped at the same height for each trial a team member measured 6’ using a tape measure and marked that position on the wall with a piece of tape. This was done to guarantee minimal variation in the height when dropping the helicopters. Randomization was demonstrated by randomly placing and selecting both the helicopters and the paper clips. The data for the experiment was as followed:
Paper Helicopter Flight Time (secs)
The average flight time for trials with one paper clip demonstrated the longest time of 1.256 seconds, the average flight time for trials with two paper clips had the second longest of 1.172, and the average flight time for trials with three paper clips was 1.002. When comparing the flight times of the trials, trial 4 had the largest average of 1.17. The paper helicopters with two paper clips fell between 0.03 and 0.18 seconds faster than the paper helicopters with one paper clip, and the paper helicopters three paper clips fell between 0.19 and 0.33 seconds faster than the paper helicopters with one paper clip.
Analysis & Results
To further investigate the experiment, a One-Way ANOVA analysis was performed. The set-up of the experiment resembled the following:
- Hypothesis
H0 : µ1 = µ2 = µ3
H1 : At least one of the µ differ
- α = 0.05
- Test of Statistic
One-Way ANOVA
SAS was used to perform the analysis. The p value for the analysis was less than .001 indicating that there was enough statistical evidence to reject the null hypothesis. Tukey test was performed to determine if there was a statistical difference between the paper clips. The Tukey test indicates there is a statistical difference between trials with 1 paper clip versus 3 and trials with 2 paper clips versus 3.
Difference
PaperClips Between Simultaneous 95%
Comparison Means Confidence Limits
1 - 2 0.06500 -0.03390 0.16390
1 - 3 0.23800 0.14522 0.33078 ***
2 - 1 -0.06500 -0.16390 0.03390
2 - 3 0.17300 0.07022 0.27578 ***
3 - 1 -0.23800 -0.33078 -0.14522 ***
3 - 2 -0.17300 -0.27578 -0.07022 ***
The plot below shows the normality of the experiment; the plot does not show signs of irregularity.
Normal Probability Plot
0.07+ ++*++
| ++*++
| * *+*+*
| ** *+*++
| ++++
| ++*+*
| ++*++*
-0.07+ ++*++
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
Conclusion
In conclusion, the hypothesis for first portion of the project stated that as the number of paper clips increased, the flight time of the helicopter would decrease. To increase the power of the experiment, the team decided to have a minimum of three trials per level. Ultimately, five trials were completed per level. When replicating this experiment, the group utilized nine different helicopters. As indicated in the data analysis section, the project group rejected the null hypothesis as the p value was less than 0.05.
Part 2. Randomized Complete Block Design
Introduction
Randomized Complete Block Design is one of the most frequently used designs in the experimentation field. The Randomized Complete Block design is the arrangement of experimental units into groups or blocks consisting of units that are similar to one another. Blocking reduces known but irrelevant sources of variation between units, thus allowing greater precision in the estimation of the source of variation under study. Since two different types of paper were used for this experiment, the group chose the paper material as the blocking factor.
This experiment analyzed how the length of tail of the helicopter affected the flight time. There were two factor levels considered; short tail length and long tail length. The team defined short tail length as the two inch reduction of the original design of the tail end of the helicopter. Long was defined as the original design of the helicopter, using the dimensions provided. The team hypothesized the helicopters with a shorter tail length would have a longer flight time than those with a longer tail length. This reasoning behind this hypothesis is due to the idea that the helicopter will be lighter overall. Secondly, a tail end that is two inches shorter than the original design should, theoretically, have farther to fall, thus increasing flight time in comparison to the original design.
Materials and Environment
The materials used to conduct this experiment include: 1 pair of scissors, three paper clips, and 6 sheets of 8.5x11’’ .01lb printable paper, 6 sheets of 8.5x11” .32lb resume paper, a ruler, and a stopwatch.
The experiment was conducted in classroom 123 of the McNair engineering building.
Methods
The proposed null hypothesis (H0 ) was there would not be a difference between the three means; the proposed alternative hypothesis (Ha ) was that at least one of the means would differ. The independent variable was the paper clips; the dependent variable was the flight time. The steps for the experiment were as followed:
- One person cut out and folded 6 paper helicopters according to the dimensions of the original design and 6 paper helicopters with 2’’ cut off the tail ends.
- The 12 paper helicopters were randomly placed on the table.
- Another person randomly selected a paper helicopter.
- The paper helicopter was then dropped at a height of 6’.
- The flight time was then recorded.
- Steps 3-5 were repeated until all the remaining helicopters were tested.
To ensure the experiment exhibited replication, one member was responsible for cutting out and folding all 12 of the helicopters, a different paper helicopter was used for each drop, and the helicopter was dropped by the same member at the same height each time. To assure that each helicopter was dropped at the same height for each trial a team member measured 6’ using a tape measure and marked that position on the wall with a piece of tape. This was done to guarantee minimal variation in the height when dropping the helicopters. Randomization was demonstrated by randomly placing and selecting the helicopters from the table. The data for the experiment was as followed:
Paper Helicopter Flight Time (secs)
The average flight time for the paper helicopters made of printer paper with a short tail was 1.23 seconds and for a long tail was 1.19. The average flight time for the paper helicopters made of resume paper with a short tail was 1.14 seconds and with a long tail was 1.08 seconds. The paper helicopters with a longer tail length fell almost 5% faster than those with a short tail. Also, the resume paper-made helicopters fall 8% faster than those made of printer paper.
Analysis & Results
To further investigate the experiment, a One-Way ANOVA analysis was performed. The set-up of the experiment resembled the following:
- Hypothesis
H0 : µ1 = µ2
H1 : µ1 > µ2
- α = 0.05
- Test of Statistic
One-Way ANOVA
SAS was used to perform the analysis. The p value for the analysis was less than .0001 indicating that there was enough statistical evidence to reject the null hypothesis. A Tukey test was performed to see if there was any difference between the trials; the chart below shows there was a statistical difference between the tail lengths of the helicopters.
Tukey Grouping Mean N Length
A 1.18833 6 Short
B 1.13167 6 Long
The plot below shows the normality of the experiment; the plot does not show signs of irregularity.
Normal Probability Plot
0.035+ *++++++
| +++++
| *++*++*
0.005+ +*+*++
| ++*+*
| +++*++*
-0.025+ *++++*
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
Conclusion
After thorough testing using a Randomized Complete Block design for the second portion of the project, the original hypothesis proved accurate. The helicopters with a shorter tail length had a longer flight time, considering the blocking factor of paper stock. The team decided to conduct six trials for increased power of the experiment. The principles of replication and randomization were implemented in this section of the project. To exhibit replication, one team member constructed every test helicopter. By doing this, variance in the physical design of the helicopters was reduced. To randomize the experiment, the helicopters were all placed on a table and randomly picked to test. The SAS output showed that the p value was less than .0001. Therefore, there was enough statistical evidence to reject the null hypothesis.