Question

An article contained the following observations on degree of polymerization for paper specimens for which viscosity times concentration fell in a certain middle range. 418 421 421 422 425 427 431 434 437 439 446 447 448 453 454 462 465

The article also gave the following observations on degree of polymerization for specimens having viscosity times concentration in a higher range. 429 430 430 431 436 438 440 441 445 446 447

(a) Construct a comparative boxplot for the two samples.

A)Comment on any interesting features.

B)The median of the high-range data is much larger than the median of the mid-range data. However, the variability present in the two boxplots seems similar.

C)The medians of the boxplots seem similar. However, the mid-range data shows much more variation compared to the high-range data.

D)The median of the mid-range data is much larger than the median of the high-range data. In addition, the mid-range data shows much more variation compared to the high-range data.

E)The medians of the boxplots seem similar. However, the high-range data shows much more variation compared to the mid-range data.

F)The median of the high-range data is much larger than the median of the mid-range data. In addition, the high-range data shows much more variation compared to the mid-range data.

(b) Calculate a 95% confidence interval for the difference between true average degree of polymerization for the middle range and that for the high range. (Use μ1 − μ2 where μ1 is the true average degree of polymerization for the middle range and μ2 is the true average degree of polymerization for high range. Round your answers to two decimal places.)

( , ) kg

Answer 1

From middle range data , five number summary are

minimum =418

first quartile = 423.5

median = 437

third quartile= 450.5

maximum = 465

From high range data , five number summary are

minimum =429

first quartile = 430

median = 438

third quartile= 445

maximum = 447

Comparative box plot :

Blue : mid range , Orange : high range

The interesting feature is

C. the medians of box plot seems similar . However mid range data shows much more variation compared to high range data.

(b) The 95% confidence interval for difference between true averages

where

and

Therefore , s= 12.54

df = 17+11-2=26

For 95% confidence level ,

Therefore 95% confidence interval is

=(-9.31, 10.68)

Therefore 95% confidence interval is .(-9.31, 10.68)