of various intensities and frequencies. Of these 45 listeners, 15 had normal hearing, 15 use at low frequencies (but didn't use hearing aids). Here is a summary of the data obtained fo sone values corresponding to this tone). Sample size Sample Sample Groups mean variance Normal hearing 15 2.41 0.1 Hearing aid 15 2.01 0.4 Some hearing 15 1.98 0.1 loss Send data to calculator Are there differences in the mean sone values for this tone for the populations of listeners aids, and listeners with low-frequency hearing loss? We can perform a one-way, independe question. Such a test uses the following statistic. Variation between the samples F= Variation vithin the samples For the data summarized above, F 3.81. (a) Give the numerator degrees of freedom of this F statistic. (b) Give the denominator degrees of freedom of this F statistic. (c) Based on these data, and using the 0.01 level of significance, should you cònclude that there are differences in the mean sone values for this tone Yes O No among the three groups?

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
Question
Much is still to be learned about the relationship between sound frequency and loudness. One way to study this relationship 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.
You have in front of you data from an experimental study in which 45 listeners were asked to perform such loudness judgments for tones
of various intensities and frequencies. Of these 45 listeners, 15 had normal hearing, 15 used hearing aids, and 15 had some hearing loss
at low frequencies (but didn't use hearing aids). Here is a summary of the data obtained for a 50 dB SPL, 500-Hz tone (the data are the
sone values corresponding to this tone).
Sample
size
Sample
Sample
variance
Groups
mean
Normal hearing
15
2.41
0.1
Hearing aid
15
2.01
0.4
Some hearing
15
1.98
0.1
loss
Send data to calculator
Are there differences in the mean sone values for this tone for the populations of listeners with normal hearing, listeners with hearing
aids, and listeners with low-frequency hearing loss? We can perform a one-way, independent-samples ANOVA test to answer this
question. Such a test uses the following statistic.
Variation between the samples
F=
Variation within the samples
For the data summarized above, F 3.81.
(a) Give the numerator degrees of freedom of this F
statistic.
(b) Give the denominator degrees of freedom of this F
statistic.
(c) Based on these data, and using the 0.01 level of
Transcribed Image Text:Much is still to be learned about the relationship between sound frequency and loudness. One way to study this relationship 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. You have in front of you data from an experimental study in which 45 listeners were asked to perform such loudness judgments for tones of various intensities and frequencies. Of these 45 listeners, 15 had normal hearing, 15 used hearing aids, and 15 had some hearing loss at low frequencies (but didn't use hearing aids). Here is a summary of the data obtained for a 50 dB SPL, 500-Hz tone (the data are the sone values corresponding to this tone). Sample size Sample Sample variance Groups mean Normal hearing 15 2.41 0.1 Hearing aid 15 2.01 0.4 Some hearing 15 1.98 0.1 loss Send data to calculator Are there differences in the mean sone values for this tone for the populations of listeners with normal hearing, listeners with hearing aids, and listeners with low-frequency hearing loss? We can perform a one-way, independent-samples ANOVA test to answer this question. Such a test uses the following statistic. Variation between the samples F= Variation within the samples For the data summarized above, F 3.81. (a) Give the numerator degrees of freedom of this F statistic. (b) Give the denominator degrees of freedom of this F statistic. (c) Based on these data, and using the 0.01 level of
15
of various intensities and frequencies. Of these 45 listeners, 15 had normal hearing, 15 used hearing aids, and 15 had some hearing loss
at low frequencies (but didn't use hearing aids). Here is a summary of the data obtained for a 50 dB SPL, 500-Hz tone (the data are the
sone values corresponding to this tone).
Sample
Sample
Sample
variance
Groups
size
mean
Normal hearing
15
2.41
0.1
Hearing aid
15
2.01
0.4
Some hearing
1.98
0.1-
loss
Send data to calculator
Are there differences in the mean sone values for this tone for the populations of listeners with normal hearing, listeners with hearing
aids, and listeners with low-frequency hearing loss? We can perform a one-way, independent-samples ANOVA test to answer this
question. Such a test uses the following statistic.
Variation between the samples
F=
Variation within the samples
For the data summarized above, F 3.81.
(a) Give the numerator degrees of freedom of this F
statistic.
(b) Give the denominator degrees of freedom of this F
statistic.
(c) Based on these data, and using the 0.01 level of
significance, should you cònclude that there are
differences in the mean sone values for this tone
O Yes O No
among the three groups?
Transcribed Image Text:15 of various intensities and frequencies. Of these 45 listeners, 15 had normal hearing, 15 used hearing aids, and 15 had some hearing loss at low frequencies (but didn't use hearing aids). Here is a summary of the data obtained for a 50 dB SPL, 500-Hz tone (the data are the sone values corresponding to this tone). Sample Sample Sample variance Groups size mean Normal hearing 15 2.41 0.1 Hearing aid 15 2.01 0.4 Some hearing 1.98 0.1- loss Send data to calculator Are there differences in the mean sone values for this tone for the populations of listeners with normal hearing, listeners with hearing aids, and listeners with low-frequency hearing loss? We can perform a one-way, independent-samples ANOVA test to answer this question. Such a test uses the following statistic. Variation between the samples F= Variation within the samples For the data summarized above, F 3.81. (a) Give the numerator degrees of freedom of this F statistic. (b) Give the denominator degrees of freedom of this F statistic. (c) Based on these data, and using the 0.01 level of significance, should you cònclude that there are differences in the mean sone values for this tone O Yes O No among the three groups?
Expert Solution
steps

Step by step

Solved in 5 steps

Blurred answer
Knowledge Booster
Point Estimation, Limit Theorems, Approximations, and Bounds
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
  • SEE MORE 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