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Poly(3-hydroxybutyrate) (PHB), a semicrystalline polymer
Chapter 2, 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 sustain-ability perspective, PHB offers many attractive proper-ties 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(3-1-1ydroxybutyrate) 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 sustain-ability perspective, PHB offers many attractive proper-ties 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(3-1-1ydroxybutyrate) 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:Answer: Step 1 of 2 The computation is done using the following table 2 (x - x ) Sl. No x 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 ( x ) 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 0 Range = 2.3 C b. The sample variance S2 from the definition (Hint: First subtract 180 from each observation.] (x x ) 2 s = n 1 = 5.2472 10 = 0.5247