Disclaimer: This study was done in an AP Statistics course with relatively small sample sizes. The validity of such studies must always be questioned. Please keep this in mind if you use or report the results of this study.
Abstract: The purpose of this study is to determine which of two paper airplanes has the superior plying power. The goal is to measure the distance flown by each plane then compare the average distance flown of both. The null hypothesis is that there is no difference between the average distance flown by plane A and the average distance flown by plane B. The alternative hypothesis is that there is a difference between the average distance flown by each plane. We will be sampling from two different paper plane and perform an inference for the mean. To do this we will conduct a t test.
The goal of this experiment is to determine which of two paper airplanes flies the farthest. To obtain the samples the study will be conducted in the hallways of Tates Creek High School to limit the effects of wind and air. Each plane will be thrown fifty times to determine an accurate mean distance for each plane. To achieve the most accurate results the same person threw the plane each time so that the force applied would be approximately the same each time. To measure the distance flown measurements were taken from the point where the plane was thrown to the farthest point it went.
|
tTest of Differences Between Two
Means |
|
|
|
|
|
|
|
Mean Group 1 |
40.1169 |
|
|
S Group 1 |
27.0896 |
|
|
n Group 1 |
50 |
|
|
df Group 1 |
49 |
|
|
Mean Group 2 |
44.7033 |
|
|
S Group 2 |
64.22139 |
|
|
n Group 2 |
50 |
|
|
df Group 2 |
49 |
|
|
Hypothesized Difference |
0 |
|
|
alpha level |
0.05 |
|
|
Total df |
98 |
|
|
Pooled Variance |
2429.116681 |
|
|
Difference in Sample Means |
4.5864 |
|
|
t-Test Statistic |
0.4652836 |
|
|
Two-Tailed Test |
|
|
|
Lower Critical Value |
-1.984467417 |
|
|
Upper Critical Value |
1.984467417 |
|
|
p-Value |
0.64276066 |
|
|
Decision |
Do Not Reject |
|
|
Plane A |
Plane B |
|
31’2” |
46” |
|
35’8” |
47’4” |
|
38’9” |
45’11” |
|
45’1” |
42’10” |
|
37’10” |
35’11” |
|
42’4” |
35’5” |
|
52” |
38’9” |
|
39’5” |
41’10” |
|
38’6” |
43’7” |
|
33’10” |
39’6” |
|
42” |
31’7” |
|
40’2” |
30’11” |
|
37’7” |
34’9” |
|
39’10” |
34’2” |
|
40’6” |
41’9” |
|
43’11” |
35’7” |
|
42’7” |
42’8” |
|
44’1” |
48’10” |
|
31’10” |
52’6” |
|
42’10” |
50’6” |
|
44’2” |
44’1” |
|
41’8” |
58” |
|
43’1” |
52’1” |
|
47’6” |
48” |
|
41’6” |
57’6” |
|
43’6” |
38’4” |
|
41’11” |
54’6” |
|
32’9” |
49’11” |
|
44’11” |
52’2” |
|
42’4” |
45” |
|
40’5” |
42’1” |
|
40’1” |
41’11” |
|
40’6” |
61’10” |
|
41’6” |
59’4” |
|
40’11” |
63’2” |
|
41’3” |
39” |
|
42’9” |
41’4” |
|
31’4” |
40’3” |
|
46’8” |
31’8” |
|
40’5” |
33’7” |
|
47” |
41’6” |
|
45’1” |
53’2” |
|
38’5” |
51’8” |
|
23’1” |
48’3” |
|
42’2” |
48” |
|
38’2” |
41’1” |
|
45’2” |
46’10” |
|
30’2” |
48’11” |
|
39’7” |
50’4” |
|
32” |
37’2” |
Analysis and Inference
Assumptions:
Hypotheses:
Test Statistic:
P-value:
df = 50 – 1 = 49
Conclusions:
The p-value is greater than .5 so the data gives no evidence that there is a significant difference between the two planes.