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Much is still to be learned about the relationship between sound frequency and loudness. One way to study the relationship between sound frequency and loudness is to have listeners perform loudness judgments for tones of different frequencies. For each listener, the output of these judgments is a number, measured in sones, that gives the loudness of the tone relative to the loudness of a reference tone. Suppose that you have in front of you data from an experimental study in which listeners were asked to perform such loudness judgments for tones of various intensities and frequencies. The listeners were divided into non-overlapping groups according to their hearing ability ("normal, unaided hearing," "some hearing loss at certain frequencies," "normal, aided hearing," etc.). The data give the sone measurements for each listener for a 50 dB SPL, 500-Hz tone. You perform a one-way, independent-samples ANOVA test of the hypothesis that the mean sone measurement are equal for the different populations of listeners represented in the study. (a) This ANOVA test is summarized in the ANOVA table below. Fill in the missing value of this ANOVA table (round your answer to at least two decimal places) Source of Degrees of Sum of Mean square F statistic variation freedom squares Between 4 1.33 0.33 groups Error (within 75 19.95 0.27 groups) Total 79 21.28

Much is still to be learned about the relationship between sound frequency and loudness. One way to study the relationship between sound frequency and loudness is to have listeners perform loudness judgments for tones of different frequencies. For each listener, the output of these judgments is a number, measured in sones, that gives the loudness of the tone relative to the loudness of a reference tone. Suppose that you have in front of you data from an experimental study in which listeners were asked to perform such loudness judgments for tones of various intensities and frequencies. The listeners were divided into non-overlapping groups according to their hearing ability ("normal, unaided hearing," "some hearing loss at certain frequencies," "normal, aided hearing," etc.). The data give the sone measurements for each listener for a 50 dB SPL, 500-Hz tone. You perform a one-way, independent-samples ANOVA test of the hypothesis that the mean sone measurement are equal for the different populations of listeners represented in the study. (a) This ANOVA test is summarized in the ANOVA table below. Fill in the missing value of this ANOVA table (round your answer to at least two decimal places) Source of Degrees of Sum of Mean square F statistic variation freedom squares Between 4 1.33 0.33 groups Error (within 75 19.95 0.27 groups) Total 79 21.28

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 23PPS
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Much is still to be learned about the relationship between sound frequency and loudness. One way to study the relationship between sound frequency and loudness is to have listeners perform loudness judgments for tones of different frequencies. For each listener, the output of these judgments is a number, measured in sones, that gives the loudness of the tone relative to the loudness of a reference tone. Suppose that you have in front of you data from an experimental study in which listeners were asked to perform such loudness judgments for tones of various intensities and frequencies. The listeners were divided into non-overlapping groups according to their hearing ability ("normal, unaided hearing," "some hearing loss at certain frequencies," "normal, aided hearing," etc.). The data give the sone measurements for each listener for a 50 dB SPL, 500-Hz tone. You perform a one-way, independent-samples ANOVA test of the hypothesis that the mean sone measurement are equal for the different populations of listeners represented in the study. (a) This ANOVA test is summarized in the ANOVA table below. Fill in the missing value of this ANOVA table (round your answer to at least two decimal places) Source of Degrees of Sum of Mean square F statistic ? variation freedom squares Between 4 1.33 0.33 groups Error 19.95 0.27 (within groups) 75 Total 79 21.28
Transcribed Image Text:Much is still to be learned about the relationship between sound frequency and loudness. One way to study the relationship between sound frequency and loudness is to have listeners perform loudness judgments for tones of different frequencies. For each listener, the output of these judgments is a number, measured in sones, that gives the loudness of the tone relative to the loudness of a reference tone. Suppose that you have in front of you data from an experimental study in which listeners were asked to perform such loudness judgments for tones of various intensities and frequencies. The listeners were divided into non-overlapping groups according to their hearing ability ("normal, unaided hearing," "some hearing loss at certain frequencies," "normal, aided hearing," etc.). The data give the sone measurements for each listener for a 50 dB SPL, 500-Hz tone. You perform a one-way, independent-samples ANOVA test of the hypothesis that the mean sone measurement are equal for the different populations of listeners represented in the study. (a) This ANOVA test is summarized in the ANOVA table below. Fill in the missing value of this ANOVA table (round your answer to at least two decimal places) Source of Degrees of Sum of Mean square F statistic ? variation freedom squares Between 4 1.33 0.33 groups Error 19.95 0.27 (within groups) 75 Total 79 21.28
(b) How many listeners total were tested in the experiment? (c) For the ANOVA test, it is assumed that the population variances of sone values for this tone are equal for each population of listeners represented. What is an unbiased estimate of this common population variance based on the sample variances? (d) Using the 0.05 level of significance, what is the critical value of the F statistic for the ANOVA test? Round your answer to at least two decimal places. (e) Using the 0.05 level of significance, do you conclude that there are differences in the mean sone values for this tone for the three populations of listeners? Yes ONo
Transcribed Image Text:(b) How many listeners total were tested in the experiment? (c) For the ANOVA test, it is assumed that the population variances of sone values for this tone are equal for each population of listeners represented. What is an unbiased estimate of this common population variance based on the sample variances? (d) Using the 0.05 level of significance, what is the critical value of the F statistic for the ANOVA test? Round your answer to at least two decimal places. (e) Using the 0.05 level of significance, do you conclude that there are differences in the mean sone values for this tone for the three populations of listeners? Yes ONo
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