Mean Computation & Dot Plot | Introduction to Statistics and Data Analysis | Probability & Statistics for Engineers & Scientists | Walpole | Problem 1.6


The tensile strength of silicone rubber is thought to be a function of curing temperature. A study was carried out in which samples of 12 specimens of the rubber were prepared using curing temperatures of 20° C and 45° C. The data below show the tensile strength values in megapascals.

20° C: 2.07 2.14 2.22 2.03 2.21 2.03
2.05 2.18 2.09 2.14 2.11 2.02
45° C: 2.52 2.15 2.49 2.03 2.37 2.05
1.99 2.42 2.08 2.42 2.29 2.01

(a) Show a dot plot of the data with both low and high temperature tensile strength values.

(b) Compute sample mean tensile strength for both samples.

(c) Does it appear as if curing temperature has an influence on tensile strength based on the plot? Comment further.

(d) Does anything else appear to be influenced by an increase in cure temperature? Explain


Solution:

Part (a)

A dot plot is shown below

5

In the figure, “×” represents the 20°C group and “◦” represents the 45°C group.


Part (b)

The mean of the 20°C group is

\displaystyle \overline{x}_{20^{\circ} C}=2.1075

The mean of the 45°C group is

\displaystyle \overline{x}_{45^{\circ} C}=2.2350


Part (c)

Based on the plot, it seems that high temperature yields more high values of tensile strength, along with a few low values of tensile strength. Overall, the temperature does have an influence on the tensile strength.


Part (d)

It also seems that the variation of the tensile strength gets larger when the cure temperature is increased.