Question

Poly(3 hydroxybutyrat expensive to produce than standard plastics. The accompanying data on melting point (oC) for each of 12 specimens of the polymer using a differential scanning calorimeter appeared in an articdle te) (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 180.6 181.7 180.8 181.5 182.5 181.6 181.4 182.1 182.2 180.4 181.6 180.4 Compute the following. (Round your answers to two decimal places.) (a) the sample range oC (b) the sample variance s from the definition [Hint: First subtract 180 from each observation.) (c) the sample standard deviation (d) s using the shortcut method

Would anyone mind helping me with this? Thanks!

Answer 1

a)The difference between the highest and lowest value of a dataset is known as range.

Highest value of the dataset=182.5

lowest value of the dataset=180.4

Range=182.5-180.4=2.1

Sample range=2.1⁰C

b)The sample variance s²

Formula to find sample variance is

where N is the total no.of observations

s²=0.5018

c)To find sample standard deviation s

we found s²=0.5018

Hence,

s=0.7084

d)s² using the shortcut method formula which is given below

s² =(29.04-(16.8^2/12))/12-1

s² =5.52/11

s²=0.5018