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Elementary Statistics

Found in: Page 191

Book edition 9th

Author(s) Weiss, Neil

Pages 590 pages

ISBN 9780321989505

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Short Answer

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 $(b)$ and $(c)$ .

(a) The linear correlation coefficient is not an adequate descriptive metric for the data.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given Information

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

Step 2: Explanation

Using an ocular approach and a television screen method, ten observers tallied the data of twenty samples of variable fibre density.

$\begin{array}{l} EYE PIECE & TV \\ 3.5 & 1.8 \\ 4.5 & 7.4 \\ 6.8 & 3.2 \\ 7.9 & 8.8 \\ 9.3 & 11.5 \\ 13.8 & 5.6 \\ 18.3 & 23.9 \end{array}$

$\begin{array}{l} 20.8 & 46.6 \\ 23.1 & 21.7 \\ 49.5 & 84.6 \\ 56.3 & 55.4 \\ 89.2 & 115.8 \\ 105.1 & 92.4 \end{array}$

$\begin{array}{l} 116.1 & 182.4 \\ 145.2 & 135.7 \\ 201.5 & 261.4 \\ 224.8 & 89.6 \\ 250.5 & 194.7 \\ 265 & 314.9 \\ 307.9 & 300.4 \end{array}$

Step 3: Explanation

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

Because the observations on the Eye Piece technique and the TV screen methods create a quadratic pattern, it is not realistic to draw a regression line for the data from the preceding scatterplot. As a result, there is no linear trend in the data. As a result, portions (b) through (c) will be omitted.

Most popular questions for Math Textbooks

Birdies and Score. The data from Exercise 4.70 for number of birdies during a tournament and final score for $63$ women golfers are on the WeissStats site.

a. decide whether use of the linear correlation coefficient as a descriptive measure for the data is appropriate, If so, then also do parts (b) and (c).

b. obtain the linear correlation coefficient.

c. interpret the value of $r$ in terms of the linear relationship between the two variables in question.

Answer true or false to the following statement, and explain your answer: A strong correlation between two variables doesn't necessมilly mean that they"re causally related.

In Exercise 4.10, we give linear equations. For each equation,

a. find the $y$ -intercept and slope.

b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation.

c. use two points to graph the equation.

$y = - 0.75 x - 5$

In Exercise 4.9, we give linear equations. For each equation,

a. find the $y$ -intercept and slope.

b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation.

c. use two points to graph the equation.

Given equation is,

$y = 0.5 x - 2$

The symbol that is used for the linear correlation coefficient is -------

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