Poly(3-hydroxybutyrate) (PHB), a semicrystalline polymer that is fully biodegrad
ID: 3131526 • Letter: P
Question
Poly(3-hydroxybutyrate) (PHB), a semicrystalline polymer that is fully biodegradable and biocompat ible, is obtained from renewable resources. From a sustainability perspective, PHB offers many attrac tive properties though it is more expensive to pro duce 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 scan ning 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.
180.5 181.7 180.9 181.6 182.6 181.6 181.3 182.1 182.1 180.3 181.7 180.5
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 evi dence for concluding that true average melting point exceeds 181°C? Carry out a test ofhypotheses using a significance level of .05.
Explanation / Answer
Formulating the null and alternative hypotheses,
Ho: u <= 181
Ha: u > 181
As we can see, this is a right tailed test.
Thus, getting the critical t,
df = n - 1 = 11
tcrit = + 1.795884819
Getting the test statistic, as
X = sample mean = 181.4
uo = hypothesized mean = 181
n = sample size = 12
s = standard deviation = 0.7242
Thus, t = (X - uo) * sqrt(n) / s = 1.913339749
Also, the p value is
p = 0.041037359
As t > 1.796, and P < 0.05, we REJECT THE NULL HYPOTHESIS.
Hence, there is compelling evidence for concluding that true average melting point exceeds 181°C at 0.05 level. [CONCLUSION]