Weber's law, a concept taught in most Introduction to Psychology courses, states that the ratio of the intensity of a stimulus to the "just noticeable" increment in intensity is constant, that is, the ratio doesn't depend on the intensity of the stimulus. The ratio is called the "Weber fraction," so a concise statement of Weber's law is that "the Weber fraction is constant, regardless of the stimulus intensity." It turns out that Weber's law is not so much a law as it is a rule of thumb, since it is violated in many situations. For instance, for some auditory stimuli, the Weber fraction does depend systematically on the stimulus intensity.   The following bivariate data are the experimental data obtained for one listener in an auditory intensity discrimination task. For each of the ten stimulus intensities  x  (in decibels), the Weber fraction  y  (in decibels) is shown. Figure 1 is a scatter plot of the data. Also given are the products of the stimulus intensities and Weber fractions for each of the ten stimuli. (These products, written in the column labelled " xy ," may aid in calculations.)   Stimulus intensity, x (in decibels) Weber fraction, y (in decibels)   xy 35 -0.69   -24.15 40 -0.51   -20.4 45 -1.41   -63.45 50 -1.22   -61 55 -2.14   -117.7 60 -2.73   -163.8 65 -3.31   -215.15 70 -3.22   -225.4 75 -4.10   -307.5 80 -4.27   -341.6        y 1 0 -1 -2 -3 -4 -5 x 30 40 50 60 70 80 90                          Figure 1       Answer the following. Carry your intermediate computations to at least four decimal places, and round your answer as specified below.   What is the value of the sample correlation coefficient for these data? Round your answer to at least three decimal places.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
icon
Concept explainers
Topic Video
Question
Weber's law, a concept taught in most Introduction to Psychology courses, states that the ratio of the intensity of a stimulus to the "just noticeable" increment in intensity is constant, that is, the ratio doesn't depend on the intensity of the stimulus. The ratio is called the "Weber fraction," so a concise statement of Weber's law is that "the Weber fraction is constant, regardless of the stimulus intensity." It turns out that Weber's law is not so much a law as it is a rule of thumb, since it is violated in many situations. For instance, for some auditory stimuli, the Weber fraction does depend systematically on the stimulus intensity.

 

The following bivariate data are the experimental data obtained for one listener in an auditory intensity discrimination task. For each of the ten stimulus intensities 
x
 (in decibels), the Weber fraction 
y
 (in decibels) is shown. Figure 1 is a scatter plot of the data. Also given are the products of the stimulus intensities and Weber fractions for each of the ten stimuli. (These products, written in the column labelled "
xy
," may aid in calculations.)

 

Stimulus intensity, x
(in decibels)
Weber fraction, y
(in decibels)
  xy
35 -0.69   -24.15
40 -0.51   -20.4
45 -1.41   -63.45
50 -1.22   -61
55 -2.14   -117.7
60 -2.73   -163.8
65 -3.31   -215.15
70 -3.22   -225.4
75 -4.10   -307.5
80 -4.27   -341.6
      
y
1
0
-1
-2
-3
-4
-5
x
30
40
50
60
70
80
90
 
 
 
 
 
 
 
 
 
 
 
 
 Figure 1
 

 

 

Answer the following. Carry your intermediate computations to at least four decimal places, and round your answer as specified below.

 

What is the value of the sample correlation coefficient for these data? Round your answer to at least three decimal places.
 
 
 
 
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 9 images

Blurred answer
Knowledge Booster
Application of Algebra
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman