Price vs. Length : How Much Are You Getting For Your Money?.
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Goal: To compare runtime of a CD to it’s cost to see if there was a connection between how much music was on a disc and how much I was paying for it. I then used this data to see if the style of music had anything to do with these factors and if I was paying more because of the length or type of music.
About the data: The sample was taken from the Billboard top selling albums list. Since prices change according to release time all albums used in the data sets have
spent no less than 3 and no more than 15 weeks on the list in their category. Albums listed in more than one category were also skipped. The top 10 albums meeting these criteria were also included in the sample for each of the 5 categories; Popular, Classical, Country, Compilation Albums and Musical Theater soundtracks.
avg. time avg. cost
Classical 3601.5 20.05
Popular 3189.8 16.44
Musicals 3702.1 21.28
Country 3589.8 14.88
Compilations 3425.7 16.36
Correlation of price (ms) and Musicals = -0.045, P-Value = 0.902
Correlation of Popular and Price (p) = -0.094, P-Value = 0.796
Correlation of Price (c) and Classical = -0.140, P-Value = 0.699
Correlation of Compulations and Price (m) = 0.403, P-Value = 0.248
Correlation of price (cm) and Country = -0.009, P-Value = 0.981
From the data collected I found very little to suggest that price and length have anything to do with each other. Price had more to do with the category of the album than the length of it, musicals having the highest over all cost followed by classical. Some reasons for the price differences might be the cost of producing an orchestrated work since the number of performers tends to be higher it would make sense that the cost to the consumer would also be raised.
Difference = mu price (ms) - mu price (cm)
Estimate for difference: 6.40
95% CI for difference: (3.82, 8.98)
T-Test of difference = 0 (vs not =): T-Value = 5.23 P-Value = 0.000 DF = 17
I did however find that the difference in price between the musicals and country music was statistically significant