Much is still to be learned about the relationship between sound frequency and loudness. One way...

 

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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 39 listeners were asked to perform such loudness judgments for tones of various intensities and frequencies. Of these 39 listeners, 13 had normal hearing, 13 used hearing aids, and 13 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). Groups Sample Sample size Sample variance mean 13. 2.48 0.3 13 2.29 0.3 Normal hearing Hearing aid Some hearing loss. 13 1.81 0.2 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, F5.17. (a) Give the numerator degrees of freedom of this F 0 X 2 statistic. (b) Give the denominator degrees of freedom of this F (c) Based on these data, and using the 0.1 level of significance, should you conclude that there are differences in the mean sone values for this tone among the three groups? Yes No 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 39 listeners were asked to perform such loudness judgments for tones of various intensities and frequencies. Of these 39 listeners, 13 had normal hearing, 13 used hearing aids, and 13 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). Groups Sample Sample size Sample variance mean 13. 2.48 0.3 13 2.29 0.3 Normal hearing Hearing aid Some hearing loss. 13 1.81 0.2 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, F5.17. (a) Give the numerator degrees of freedom of this F 0 X 2 statistic. (b) Give the denominator degrees of freedom of this F (c) Based on these data, and using the 0.1 level of significance, should you conclude that there are differences in the mean sone values for this tone among the three groups? Yes No