Is the average length of a top 100 song on iTunes 180 seconds? We predicted that the average length of a top 100 song on iTunes is not equal to 180 seconds. Scientists have found that 180 seconds is where bloat starts to set in. The population that we intend for our study to represent is the top 100 songs on iTunes. The variable that we obtained during our data collection was the song length in seconds. Methods We collected our data from the Top 100 Songs section of the iTunes Store. We selected data to include in our sample by randomly choosing 30 of the top 100 songs. To avoid bias in our sample, we used a random number generator that included the numbers 1 through 100, which represented the rankings of the songs, to select 30 different songs. We believe the sample we obtained was representative of the population because it was random and included over a quarter of the population. We conducted a one-sample t-test to analyze our data. Results Our confidence level is 95% and our significance level is 5%. The point estimate is 226.933. The margin of error is 11.762. The degrees of freedom is 29. The Confidence Interval is (215.171, 238.695). We are 95% confident that the average song length of a top 100 song on iTunes falls within the interval of 215.171 to 238.695 seconds.
StatCrunch Column Mean Std. Dev. Min Max Q1 Q3 n Median Song Length (Seconds) 226.93333 31.501432 163 291 208 241 30 223 Print - Back Average Length of Top 100 Songs on iTunes Generated Dec 4, 2012 by n.anisko Nathan Anisko and Eric Anderson Introduction Is the average length of a top 100 song on iTunes 180 seconds? We predicted that the average length of a top 100 song on iTunes is not equal to 180 seconds. Scientists have found that 180 seconds is where bloat starts to set in. The population that we intend for our study to represent is the top 100 songs on iTunes. The variable that we obtained during our data collection was the song length in seconds. Methods We collected our data from the Top 100 Songs section of the iTunes Store. We selected data to include in our sample by randomly choosing 30 of the top 100 songs. To avoid bias in our sample, we used a random number generator that included the numbers 1 through 100, which represented the rankings of the songs, to select 30 different songs. We believe the sample we obtained was representative of the population because it was random and included over a quarter of the population. We conducted a one-sample t-test to analyze our data. Results Our confidence level is 95% and our significance level is 5%. The point estimate is 226.933. The margin of error is 11.762. The degrees of freedom is 29. The Confidence Interval is (215.171, 238.695). We are 95% confident that the average song length of a top 100 song on iTunes falls within the interval of 215.171 to 238.695 seconds. Conclusions The average length of a top 100 song on iTunes does not equal 180 seconds. Our analyses support our expected findings. The 95% Confidence Interval does not contain the assumed value of 180 seconds. This challenge is statistically significant at the 5% significance level. As a result of our study, we can draw the conclusion that the average length of a top 100 song on iTunes is much greater than 180 seconds. From this project, we learned that the top 100 songs on iTunes contain a wide range of genres, the song lengths can differ by a large amount, and the one-sample t-test is useful to determine whether a stated value is accurate among a population. Result 1: Song Lengths Table [Info] Summary statistics: Result 2: Song Lengths Chart [Info] StatCrunch https://www.statcrunch.com/5.0/printreport.php?reportid=28647&group... 1 of 2 1/26/2018, 10:26 AM StatCrunch https://www.statcrunch.com/5.0/printreport.php?reportid=28647&group... 2 of 2 1/26/2018, 10:26 AM Ritchie_music iTunes Song NumberGenreSong length (seconds)Histogram Exploratory Data Analysis / Descriptive Statistics Measures of center: Sample Mean Median Modal class Minimum Maximum First Quartile (Q1) Third Quartile (Q3) Measures of variablility (spread or dispersion) Sample Standard Deviation Range = Max - Min IQR = Q3 - Q1 Identify Outliers Lower boundary =Q1 - 1.5*IQR Upper boundary = Q3 + 1.5*IQR Symmetry Skewness MTH 1501 – Statistics I Final Project Part 1 Name(s): _______________________________________ A. Literature Review and Research Question: Read the following articles: Average Length of Top 100 Songs on iTunes by Nathan Anisko and Eric Anderson (available in Moodle classroom) Why are Songs on the Radio about the Same Length by Rhett Allain: https://www.wired.com/2014/07/why-are-songs-on-the-radio-about-the-same-length/ Interactive Plot of Average Song Length Over Time: https://chart-studio.plotly.com/~RhettAllain/131/average-song-length/#/ B. Research Question: Example: Is the average length of songs on iTunes list of top 100 songs in 2018 significantly different from the average song length, 234.5 seconds, in 2008? State your Research Question: (Write this statement after completing the Excel data sheet.) C. Select a random sample (n = 40) Select a random sample of 40 songs from one of the “Top 100” websites below by using your TI-84 calculator (instructions on the next page) or your computer Google Random Number Generator to generate random numbers between 1 and 100. No song should be sampled more than once. Instructions for random number generator using your computer: Use the link above. There are both a dynamic method and an old method shown. The old method (found near the middle of the page) may be the easiest. If using the old method, you will need to ‘freeze’ the list so that it does not change on its own. Follow their instructions to create the random list in column ‘A’. THEN - Copy column ‘A’ and paste-special into column ‘C’. This will freeze the random list in column ‘C’ so that you can use it for selecting your song list. (NOTE: Columns ‘A’ and ‘B’ will continue to change while you are using the spreadsheet, this is normal. Column ‘C’ will not change as long as you used paste-special during the copy process.) Instructions for random number generation using the TI-84: “Top 100” websites: iTunes top 100 songs 2020 http://www.popvortex.com/music/charts/top-100-songs.php Apple Music Top 100: USA https://music.apple.com/us/playlist/top-100-usa/pl.606afcbb70264d2eb2b51d8dbcfa6a12 Apple Music Top 100: Global https://music.apple.com/us/playlist/top-100 global/pl.d25f5d1181894928af76c85c967f8f31 Record the iTunes song number, which you have randomly selected, song title, genre and song length (seconds) in the chart below. (NOTE: As an alternative you can record the information directly into the Excel template and then copy the list here. Please replace the empty table below with your completed Excel table.) Count iTunes1 Song # Song Title Genre Length (sec)2 EX 7 Dance Monkey Alternative 210 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 Notes: 1 Each song should be listed only once. 2 The song length must be converted to seconds. D. Set up an Excel data file for your sampled data. An Excel template can be found under the assignment link on Moodle. E. Exploratory Data Analysis Visualize: Create a histogram for the variable, song length. Be sure to title your graph and label each axis. Copy and paste your histogram in the space below. Run all appropriate descriptive statistics for the variable song length See details on Excel template Copy and paste the results of your analysis in the space below: Interpret Skewness: If skewness is positive, the data are positively skewed or skewed right, meaning that the right tail of the distribution is longer than the left. If skewness is negative, the data are negatively skewed or skewed left, meaning that the left tail is longer. If skewness = 0, the data are perfectly symmetrical, unlikely for real-world data. Bulmer (1979) suggested the following rule for interpreting skewness. · If skewness is less than −1 or greater than +1, the distribution is highly skewed. · If skewness is between −1 and −½ or between +½ and +1, the distribution is moderately skewed. · If skewness is between −½ and +½, the distribution is approximately symmetric. Important note: This rule applies to your data only. The sample skewness does not necessarily apply to the whole population. Describe the shape for the distribution of your data: F. Submit the following items via the Final Project Part 1 assignment link on Moodle. · Your Excel data file, which should include the supporting work for your Exploratory Data Analysis. · This completed Word document Reminder: Your Final Project cannot be graded if your Excel data file has not been submitted. MTH 1501 – Statistics I Final Project Part 2 Name: _______________________________________ A. Inferential Statistics: One-sample test for the mean (40 points) Decision Map: One-sample test for the mean Perform a 1-sample z-test for the mean. Use a 2-tail test at = 0.05. Test Assumptions: 1-sample z-test for the mean. · Study-design assumption: Simple random sampling · Data-related assumption: Parent population was normally distribution or the sample size is sufficiently large. Note: n = 30 is the minimum sample size that should be considered sufficiently large for the Central Limit Theorem to apply. Central Limit Theorem Simulation State Research Question: State Hypotheses for the study: Ho: H1: Starting assumption: Null hypothesis is true. Sketch the distribution, find the critical values and state your decision criteria (i.e., When can the null hypothesis be rejected?) Calculate the test statistic: Reason and Decision regarding Ho: Conclusion: B. Write a paragraph summarizing your results, making sure to: · State your research question and the hypothesis test performed as part of your inferential analysis. · Describe your distribution. Is the distribution roughly symmetric or skewed (right or left)? If skewed, is the distribution strongly/highly or moderately skewed? · Identify any outliers in the distribution. · If the distribution of your data is skewed, report both the Mean, along with the standard deviation, and the median, along with the IQR. · Discuss whether the test assumptions were assumed to have been satisfied. · Report the results of your inferential analysis. C. Submit this completed Word document via the Final Project Part 2 assignment link on Moodle. Please submit your work in Word (.docx) format. Important Reminders: · Your Final Project cannot be graded if your Excel data file has not been submitted. · Other items must be submitted as Word documents in order to be graded. Failure to do so may result in late deductions. Project – Part 1 Project – Part 1 Project – Part 1 Apr 18 - 24 MTH-1501 Final Project – Top 100 Songs Number one on Apple’s Top 100 song list is, “Solid” by Young Thug & Gunna. Apparently, this compilation by a top rap singer Young Stoner and his cohort Gunna, is their second top 100 album. With my aged ears I had to resort to noise cancelling headphones to understand the lyrics,