The article cited in Exercise 25 of Section 8.2 gave the following data on mass crystallinity (in %) for 12 samples of the PHB polymer:
a. Is it plausible that the mass crystallinity for this type of polymer is normally distributed?
b. Suppose researchers wanted to investigate whether the true average mass crystallinity exceeds 40%. Carry out a test of appropriate hypotheses using a significance level of .05.
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 authors of “The Melting Behaviour of Poly(3-Hydroxybutyrate) by DSC. Reproducibility Study” (Polymer Testing, 2013: 215–220) wanted to investigate various physical properties of PHB by using a differential scanning calorimeter (DSC).
For each of 12 PHB specimens, the authors used a DSC to measure the melting point (in °C) of the polymer, which is the temperature for 99% completion of the fusion process.
A normal probability plot of the data shows a reasonably linear pattern, so it is plausible that the population distribution of PHB melting points as measured by DSC is at least approximately normal. The sample mean and standard deviation are 181.4 and .7242, respectively. Is there compelling evidence for concluding that true average melting point exceeds 181°C? Carry out a test of hypotheses using a significance level of .05.