Is commercially recorded music getting louder over time? Some music critics think so. An online database has been compiled by individuals around the world and currently contains data for over 100,000 albums, going back to the 1940’s. Two independent random samples, of size 100 albums each, were taken from this data. The first sample was drawn from albums released between 1980 and 1999. These albums had an average loudness of 68.3 dB, with an SD of 2.6 dB. The second sample was drawn from albums released between 2000 and 2019. These albums had an average loudness of 69.1 dB, with an SD of 2.8 dB. (Increasing dB indicates louder albums.) We will test the null hypothesis that the average loudness of all albums in the database released 1980-1999 is the same as those in the database released 2000-2019, versus the alternative that they are different. (a) Under the null hypothesis, the difference in the sample averages is expected to be _________ dB. The standard error for the difference is estimated to be _________ dB. (b) The two-sample z test statistic is _________. (c) The p-value is _________. (d) What do you conclude?
Is commercially recorded music getting louder over time? Some music critics think so.
An online database has been compiled by individuals around the world and currently
contains data for over 100,000 albums, going back to the 1940’s. Two independent
random samples, of size 100 albums each, were taken from this data. The first sample
was drawn from albums released between 1980 and 1999. These albums had an
average loudness of 68.3 dB, with an SD of 2.6 dB. The second sample was drawn from
albums released between 2000 and 2019. These albums had an average loudness of
69.1 dB, with an SD of 2.8 dB. (Increasing dB indicates louder albums.)
We will test the null hypothesis that the average loudness of all albums in the database
released 1980-1999 is the same as those in the database released 2000-2019, versus the
alternative that they are different.
(a) Under the null hypothesis, the difference in the sample averages is expected to be
_________ dB. The standard error for the difference is estimated to be _________ dB.
(b) The two-sample z test statistic is _________.
(c) The p-value is _________.
(d) What do you conclude?
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