Question

In the article "Comparison of Fiber Counting by TV Screen and Eyepieces of Phase Contrast Microscopy" (Amer. icon Industrial Hyeiene Asseciution Journal, Vol. 63, Pp. 756-761), 1. Moa et al. reported on determining fiber density by two different methods. Twenty samples of varying fiber density were each counted by 10 viewers by means of an eyepiece method and a television screen method to determine the relationship between the counts done by each method. The results, in fibers per square millimeter, are presented on the Weiss Stats site.

(a). Decide whether use of the linear correlation coefficient as a descriptive measure for the data is appropriate, If so, then also parts $\left(b\right)$and$\left(c\right)$.

Short answer

a. The linear correlation coefficient as a descriptive measure for the data is not- appropriate.

Step-by-step solution

Given Information 

Whether the use of linear correlation coefficient is appropriate or not.

Explanation 

The data of twenty samples of varying fibre-density were each counted by $10$viewers by means of an eyepiece method and a television-screen method.

$\begin{array}{|ll|}\hline \text{EYE PIECE}& \text{TV}\\ 3.5& 1.8\\ 4.5& 7.4\\ 8.8& 3.2\\ 7.9& 5.8\\ 8.3& 11.5\\ 13.8& 5.6\\ \hline\end{array}$

$\begin{array}{|ll|}\hline 18.3& 23.9\\ 20.8& 46.8\\ 23.1& 21.7\\ 49.5& 84.6\\ 86.3& 55.4\\ 89.2& 115.8\\ 105.1& 92.4\\ \hline\end{array}$

$\begin{array}{|ll|}\hline 116.1& 182.4\\ 145.2& 135.7\\ 201.5& 281.4\\ 224.8& 89.6\\ 250.5& 194.7\\ 285& 300.4\\ 307.9& 314.9\\ \hline\end{array}$

Explanation

The scatterplot for the given data can be drawn by using the MINITAB:

From the above scatterplot, it is not reasonable to find a regression line for the data because the observations regarding Eye Piece method and TV screen methods forms a quadratic pattern. Hence, there is no linear pattern visible in the given data. Therefore, the parts (b) - (c) will be omitted.