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. 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 violated in many situations. For instance, for some auditory stimuli, the Weber fraction depends 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 is the product of the stimulus intensity and the Weber fraction for each of the ten stimuli. (These products, written in the column labeled “$ xy $”, may aid in calculations.)| Stimulus Intensity, $ x $ (in decibels) | Weber Fraction, $ y $ (in decibels) | $ xy $ ||-------------------------------------------|---------------------------------------|------------|| 35 | -0.55 | -19.25 || 40 | -0.37 | -14.8 || 45 | -1.31 | -58.95 || 50 | -1.17 | -58.5 || 55 | -2.06 | -113.3 || 60 | -2.65 | -159 || 65 | -3.18 | -206.7 || 70 | -3.3 | -231 || 75 | -4.35 | -326.25 || 80 | -4.1 | -328 |Figure 1: This is a scatter plot illustrating the relationship between stimulus intensity (in decibels) along the x-axis and the Weber fraction (in decibels) along the y-axis. The plot shows a negative correlation, indicating that as stimulus intensity increases, the Weber fraction decreases.What is the sample correlation coefficient for these data? Carry your intermediate computations to at least four decimal places and round your answer to

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Answered: just notice increment in intensity is…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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An advertising firm wishes to demonstrate to its clients the effectiveness of the advertising campaigns it has conducted. The following bivariate data on twelve recent campaigns, including the cost of each campaign (denoted by x, in millions of dollars) and the resulting percentage increase in sales (denoted by y) following the campaign, were presented by the firm. A scatter plot of the data is shown in Figure 1. Campaign cost, x (in millions of dollars) Increase in sales, y (percent) 2.26 6.55 1.49 6.17 7.2+ 3.01 6.94 2.08 6.72 6.8+ it 2.03 6.49 6.6 - 3.23 6.50 6.4+ 4.04 6.98 6.2 1.29 6.33 6. 2.82 6.50 2.5 + 1.5 2 3.5 3.54 6.80 Campaign cost (in millions of dollars) 3.67 6.85 Figure 1 1.56 6.56 Send data to calculator Send data to Excel The value of the sample correlation coefficient r for these data is approximately 0.776. Answer the following. Carry your intermediate computations to at least four decimal places, and round your answers as specified below. (If necessary, consult a…
In ongoing economic analyses, the federal government compares per capita incomes not only among different states but also for the same state at different times. Typically, what the federal government finds is that "poor" states tend to stay poor and "wealthy" states tend to stay wealthy. Would we have gotten information about the 1999 per capita income for a state (denoted by y ) from its 1980 per capita income (denoted by x)? The following bivariate data give the per capita income (in thousands of dollars) for a sample of fifteen states in the years 1980 and 1999 (source: U.S. Bureau of Economic Analysis, Survey of Current Business, May 2000). The data are plotted in the scatter plot in Figure 1. Also given is the product of the 1980 per capita income and the 1999 per capita income for each of the fifteen states. (These products, written in the column labelled " xy ", may aid in calculations.) Question table 1980 per capita income, x (in $1000 s) 1999 per capita…
A cognitive psychologist conducted a study of whether familiarity of words (X) predicts the time it takes (in seconds) to press a button indicating whether the word is singular or plural (Y), with all participants being given the same words. Familiarity with these words was rated at a later time on a 7-point scale (with higher numbers indicating more familiarity). The participants' scores were: X : 6, 2, 5 ,3 ,7 Y : 0.3 , 1.5 , 0.8 , 1.4 ,0.1 a.Figure the correlation coefficient Describe the correlation Figure the linear prediction rule; list the b value, a value and the final formula Predict the time it takes to press a button if the familiarity with the word is 1
r. Lyte wishes to study speed of Reaction Time to press a button in response to the onset of a lamp. The independent variable (IV) is the color of the light produced by the lamp (red, orange, yellow, green, or blue). Since only 10 participants are available, she elects to administer the IV within-subjects with all 10 participants being exposed to all five levels of the color variable. The order of the color of the light presentation is to be counterbalanced. Using concepts from the textbook, why would Dr. Lyte need to use counterbalancing in this scenario?
Consider the following data on price ($) and the overall score for six stereo headphones tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). Brand Price ($) A B C D E F Ọ Ho Bo=0 Ha: Bo #0 OHO: B₁ ≥ 0 H₂: B₁ <0 O Ho: B₁ * 0 H₂: B₁ = 0 180 ⒸH₁: B₁ = 0 H₂: B₁ 0 150 95 70 70 35 Score 76 69 59 56 40 (a) The estimated regression equation for this data is ý = 21.926421 + 0.320736x, where x = price ($) and y = overall score. Does the t test indicate a significant relationship between price and the overall score? Use a = 0.05. State the null and alternative hypotheses. o Ho Boo Hà Bo=0 24 Find the value of the test statistic. (Round your answer to three decimal places.) 4.558263 Find the p-value. (Round your answer to four decimal places.) p-value = 0.010352 What is your conclusion? O Do not reject Ho. We cannot conclude that the relationship between price ($) and overall score is…
In ongoing economic analyses, the federal government compares per capita incomes not only among different states but also for the same state at different times. Typically, what the federal government finds is that "poor" states tend to stay poor and "wealthy" states tend to stay wealthy. Would we have gotten information about the 1999 per capita income for a state (denoted by y) from its 1980 per capita income (denoted by x)? The following bivariate data give the per capita income (in thousands of dollars) for a sample of sixteen states in the years 1980 and 1999 (source: U.S. Bureau of Economic Analysis, Survey of Current Business, May 2000). The data are plotted in the scatter plot in Figure 1. Also given is the product of the 1980 per capita income and the 1999 per capita income for each of the sixteen states. (These products, written in the column labelled "xy", may aid in calculations.) Florida Nevada West Virginia Hawaii Arkansas Utah Kansas Montana North Dakota Nebraska…
Is this correct so far?
Mr. Bates wants to compare the midterm scores of his students who took the course during the fall semester versus the spring semester. Here is the data: Fall 89 86 64 91 72 94 87 83 86 90 74 59 87 97 87 Spring 76 70 82 94 76 66 72 51 75 97 74 81 85 96 74 Can he say that there was a significant difference between his fall and spring students? (Use α = .10)
An advertising firm wishes to demonstrate to its clients the effectiveness of the advertising campaigns it has conducted. The following bivariate data on twelve recent campaigns, including the cost of each campaign (denoted by x , in millions of dollars) and the resulting percentage increase in sales (denoted by y ) following the campaign, were presented by the firm. A scatter plot of the data is shown in Figure 1. Also given are the products of the values for campaign cost and values for percentage increase in sales for each of the twelve campaigns. (These products, written in the column labelled " xy ," may aid in calculations.) Campaign cost, x(in millions of dollars) Increase in sales, y(percent) xy 3.18 6.49 20.6382 3.77 6.80 25.636 2.27 6.55 14.8685 2.30 6.79 15.617 2.06 6.50 13.39 3.79 7.09 26.8711 1.53 6.60 10.098 1.29 6.46 8.3334 1.58 6.17 9.7486 3.14 6.56 20.5984 2.86 6.84 19.5624 3.59 6.83 24.5197…
A researcher is conducting a test to see if handedness (right or left) affects the speed at which people perform a particular task. The researcher only knows the order in which the contestants finished. When the data are summarized (with R for right-handed and L for left-handed) the order of finishing (fastest to slowest) was: R, R, R, R, L, R, L, R, L, L Is there statistically significant evidence of an effect of handedness on the speed? Test statistic: The name of the statistical table, degrees of freedom (if appropriate), and the numerical value of the critical value for this test: P-value: Circle an appropriate conclusion: • There is significant evidence that left-handed contestants will finish the task faster. • We cannot reject the hypothesis that handedness has no effect on the time to finish the task. • There is significant evidence that right-handed contestants will finish the task faster.
Here are the scatter plots for two sets of bivariate data with the same response variable. The first compares the variables x & y. The second compares the variables w & y O O 00 00 + O Q Which explanatory variable has a stronger relationship with the response variable y? O The first variable (x) has a stronger relationship with the response variable y. O The second variable (w) has a stronger relationship with the response variable y.
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