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 stimulus intensities

x

(in decibels), the experimental Weber fractiony

(in decibels) is shown. For these data, the least-squares regression line is=

y

2.7902

0.0874

x

.This line is shown in the scatter plot below.Stimulus intensity,x

(in decibels)Weber fraction,y

(in decibels)35

0.51

40

0.47

45

1.34

50

1.09

55

2.02

60

2.72

65

3.12

70

3.02

75

3.95

80

4.13

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Weber fraction,y

(in decibels)

y

1

0

-1

-2

-3

-4

-5

x

30

40

50

60

70

80

90

Stimulus intensity,x

(in decibels)

Based on the sample data and the regression line, complete the following.

(a)For these data, stimulus intensities that are greater than the mean of the stimulus intensities tend to be paired with Weber fractions that are

(Choose one)

the mean of the Weber fractions.

(b)According to the regression equation, for an increase of one decibel in stimulus intensity, there is a corresponding decrease of how many decibels in the Weber fraction?

(c)From the regression equation, what is the predicted Weber fraction (in decibels) when the stimulus intensity is80

decibels? (Round your answer to at least two decimal places.)

(d)What was the observed Weber fraction (in decibels) when the stimulus intensity was80

decibels?