Transcript Comparing Density and Volume Summer Science Academy

Comparing Density and Volume
Summer Science Academy
Friday July 22, 2005
LeMoyne-Owen College
Group Four (4)
Group Members
• Marico Q. Frazier
• Timothy Renfroe
Hendaia Wondim
Ashley Gaither
Purpose
• To describe mass and volume for each
experimental item.
• To estimate the relationship between mass
and volume.
• To compare experimental and accepted
density values.
Methods
• Measure the mass of the right cylinder and the
rectangle cube
• Measure to find the radius of the cylinder and its
height to find its volume
• Measure to find the length, width, and height of
the rectangle cube to find its volume
• Divide the mass of each object by its volume to
find the experimental density
Working Hard Finding an
Answer
Measurements
Object
Wood
Group# Mass
Length Height Width Volume
1
105.1
14.55
1.9
9.04 249.91
2
47.8
7.45
2.05
4.55
69.49
3
38.2
6
2.01
4.5
54.27
4
37.6
5.48
2.05
4.54
51.00
Volume = Length * Width * Height
Descriptive Statistics
Graphical Method
300.0
Mass Volume
105.1 249.91
47.8 69.49
38.2 54.27
37.6 51.00
250.0
200.0
Mass
150.0
Volume
100.0
50.0
0.0
1
2
3
Groups
4
Density
Density = Mass / Volume
Mass Volume
105.1 249.91
47.8
69.49
38.2
54.27
37.6
51.00
Experimental Accepted Percent
Density
Density Error
0.421
0.75
78.34%
0.688
0.75
9.03%
0.704
0.75
6.55%
0.737
0.75
1.73%
Descriptive Statistics
Numerical Method
Experimental
Density
Mean
Standard Error
Median
Mode
Standard Deviation
Sample Variance
Kurtosis
Skewness
Range
Minimum
Maximum
Sum
Count
0.637382
0.073005
0.695879
#N/A
0.146009
0.021319
3.63249
-1.87973
0.316671
0.42055
0.737221
2.549529
4
Linear Regression
Mass
without intercept term
140.0
120.0
100.0
80.0
60.0
40.0
20.0
0.0
0.00
Mass
Predicted Mass
100.00 200.00 300.00
Volume
Volume
Regression Statistics
Multiple R 0.876853432
R Square
0.768871942
Adjusted R Square
0.435538608
Standard Error 15.52365732
Observations
4
Coefficients Standard Error t Stat
P-value
0.461042289 0.057522365 8.015009291 0.004054536
Hypothesis
• Null Hypothesis: Experimental &
Accepted Densities are same.
• Alternative Hypothesis: Experimental &
Accepted Densities are different.
Paired t-test
t-Test: Paired Two Sample for Means
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean Difference
df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
Experime
ntal
Accepted
Density
Density
0.637382
0.75
0.021319
0
4
4
#DIV/0!
0
3
-1.54261
0.1103
2.353363
0.220601
3.182449
P-value > 0.05. So, failed to reject null hypothesis.
Conclusion
Since we failed to reject null hypothesis,
the experimental density supports the
accepted density. Thus, we confirm the
formula, Density = Mass / Volume.