Introduction to Statistics and Data Analysis | Probability & Statistics for Engineers & Scientists | Walpole | Problem 1.3

A certain polymer is used for evacuation systems for aircraft. It is important that the polymer be re­sistant to the aging process. Twenty specimens of the polymer were used in an experiment. Ten were assigned randomly to be exposed to the accelerated batch aging process that involved exposure to high tempera­tures for 10 days. Measurements of the tensile strength of the specimens were made and the following data were recorded on tensile strength in psi.

No aging:227222218217225
218216229228221
Aging:219214215211209
218203204201205

(a) Do a dot plot of the data.

(b) From your plot, does it appear as if the aging pro­cess has had an effect on the tensile strength of this polymer? Explain.

(c) Calculate the sample mean tensile strength of the two samples.

(d) Calculate the median for both. Discuss the simi­larity or lack of similarity between the mean and median of each group.

Solution:

Part a

A dot plot is shown below.

2

In the figure, “×” represents the “No aging” group and “◦” represents the “Aging” group.

Part b

Yes; tensile strength is greatly reduced due to the aging process.

Part c

\displaystyle Mean_{aging}=209.90 and \displaystyle Mean_{No\:aging}=222.10

Part d

\displaystyle Median_{Aging}=210 and \displaystyle Median_{No\:Aging}=221.50.

The means and medians for each group are similar to each other.