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 an article. 180.6 181.8 180.8 181.6 182.7 181.6 181.2 182.2 182.2 180.3 181.8 180.5 Compute the following. (Round your answers to two decimal places.) (a) the sample range °C (b) the sample variance s2 from the definition [Hint: First subtract 180 from each observation.] s2 = (c) the sample standard deviation s = (d) s2 using the shortcut method s2 =

Answer 1

SOLUTION:-

Given data

(a).The sample range:-

180.6 181.8 180.8 181.6 182.7 181.6 181.2 182.2 182.2 180.3 181.8 180.5

Ascending order,

180.3,180.5,180.6,180.8,181.2,181.6,181.6,181.8,181.8,182.2,182.2,182.7

Min=180.3

Range=Max-Min

Range=2.4

(b).The sample variance s^2:-

Here,

n-1=11

s^2=6.4061/11

s^2=0.5826

(c).The sample standard deviation s:-

s=0.7631

(d).Calculation of s^2 by using shortcut method:-

Where,

df=11