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Solved: Poly(3-hydroxybutyrate) (PHB), a semicrystalline
Chapter 1, Problem 44E(choose chapter or problem)
Poly(3-hydroxybutyrate) (PHB), a semicrystalline polymer that is fully biodegradable and biocompatible, is obtained from renewable resources. From a sustainability perspective, PHB offers many attractive properties though it is more expensive to produce than standard plastics. The accompanying data on melting point (°C) for each of 12 specimens of the polymer using a differential scanning calorimeter appeared in the article "The Melting Behaviour of Poly(3-Hydroxybutyrate) by DSC. Reproducibility Study" (Polymer Testing, 2013: 215-220).
180.5 181.7 180.9 181.6 182.6 181.6
181.3 182.1 182.1 180.3 181.7 180.5
Compute the following:
a. The sample range
b. The sample variance S2 from the definition (Hint: First subtract 180 from each observation.)
c. The sample standard deviation
d. S2 using the shortcut method
Questions & Answers
QUESTION:
Poly(3-hydroxybutyrate) (PHB), a semicrystalline polymer that is fully biodegradable and biocompatible, is obtained from renewable resources. From a sustainability perspective, PHB offers many attractive properties though it is more expensive to produce than standard plastics. The accompanying data on melting point (°C) for each of 12 specimens of the polymer using a differential scanning calorimeter appeared in the article "The Melting Behaviour of Poly(3-Hydroxybutyrate) by DSC. Reproducibility Study" (Polymer Testing, 2013: 215-220).
180.5 181.7 180.9 181.6 182.6 181.6
181.3 182.1 182.1 180.3 181.7 180.5
Compute the following:
a. The sample range
b. The sample variance S2 from the definition (Hint: First subtract 180 from each observation.)
c. The sample standard deviation
d. S2 using the shortcut method
ANSWER:Step 1 of 4
The computation is done using the following table
Sl. No |
x |
( |
|
1 |
180.5 |
0.71487025 |
32580.25 |
2 |
181.7 |
0.12567025 |
33014.89 |
3 |
180.9 |
0.19847025 |
32724.81 |
4 |
181.6 |
0.06477025 |
32978.56 |
5 |
182.6 |
1.57377025 |
33342.76 |
6 |
181.6 |
0.06477025 |
32978.56 |
7 |
181.3 |
0.00207025 |
32869.69 |
8 |
182.1 |
0.56927025 |
33160.41 |
9 |
180.3 |
1.09307025 |
32508.09 |
10 |
181.7 |
0.12567025 |
33014.89 |
11 |
180.5 |
0.71487025 |
32580.25 |
Sum |
1994.8 |
5.24727275 |
361753.2 |
Average |
181.3455 |
We need to compute the following
a. The sample range is the difference between highest value and the lowest value.
That is, Range = 182.6 - 180.3
Range = 2.3°C