Much is still to be learned about the relationship between sound frequency and loudness. One way to study this relationship is to havelisteners 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 tonesof various intensities and frequencies. Of these 45 listeners, 15 had normal hearing, 15 used hearing aids, and 15 had some hearing lossat 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 thesone values corresponding to this tone).SamplesizeSampleSamplevarianceGroupsmeanNormal hearing152.410.1Hearing aid152.010.4Some hearing151.980.1lossSend data to calculatorAre there differences in the mean sone values for this tone for the populations of listeners with normal hearing, listeners with hearingaids, and listeners with low-frequency hearing loss? We can perform a one-way, independent-samples ANOVA test to answer thisquestion. Such a test uses the following statistic.Variation between the samplesF=Variation within the samplesFor the data summarized above, F 3.81.(a) Give the numerator degrees of freedom of this Fstatistic.(b) Give the denominator degrees of freedom of this Fstatistic.(c) Based on these data, and using the 0.01 level of 15of various intensities and frequencies. Of these 45 listeners, 15 had normal hearing, 15 used hearing aids, and 15 had some hearing lossat 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 thesone values corresponding to this tone).SampleSampleSamplevarianceGroupssizemeanNormal hearing152.410.1Hearing aid152.010.4Some hearing1.980.1-lossSend data to calculatorAre there differences in the mean sone values for this tone for the populations of listeners with normal hearing, listeners with hearingaids, and listeners with low-frequency hearing loss? We can perform a one-way, independent-samples ANOVA test to answer thisquestion. Such a test uses the following statistic.Variation between the samplesF=Variation within the samplesFor the data summarized above, F 3.81.(a) Give the numerator degrees of freedom of this Fstatistic.(b) Give the denominator degrees of freedom of this Fstatistic.(c) Based on these data, and using the 0.01 level ofsignificance, should you cònclude that there aredifferences in the mean sone values for this toneO Yes O Noamong the three groups?

Question

Accepted Answer

Given the summary data as

Groups 
Sample size
Sample mean
Sample variance

Normal hearing
15…