Alicia Strank Katharine Mitchell Alyson Wit Statistical Methods and Computing Final Project The group compared proportions of music played on radio stations WMT 96 5FM and KBEA 99 7FM Ho p1 p2 Ha p1 p2 Where p1 refers to the proportion of music played per hour on station WMT 96 5FM and p 2 refers to the proportion played on KBEA 99 7FM The group also tested whether instantaneous random sampling gives similar proportions to those found with continuous sampling H0 pc pi Ha pc pi Where pc refers to the proportion of music played per hour found with continuous sampling The proportion of music played per hour found with the instantaneous sampling is represented by p i All samples were taking between 12 00 pm and 6 00 pm to atempt to avoid variation in what might be played at different times Part 1 Instantaneous Random Sampling of 99 7FM and 96 5FM Instantaneous random sampling data was taken of KBEA 99 7FM and WMT 96 5FM The random sample times were found using www random org For collection of this data the radio was turned on at the times generated and the instantaneous state of the radio was recorded This was done for both stations at the same time for accurate comparison This data was then organized into proportions and interpreted using SAS chi square tests Raw instantaneous sampling data can been seen in Appendix A The chi square test of the instantaneous sampling shows that the two stations are not statistically different in how much music is played per hour The null hypothesis cannot be rejected This is confirmed by the high p value which is approximately 0 82 Part 2 Comparisons of Continuous Sampling and Instantaneous Sampling of 99 7FM A continuous sampling of KBEA 99 7FM and compared to the instantaneous sampling from the same station The continuous sample data can be seen in Appendix B The proportions of music played each hour were used in the SAS calculations Proc means was used to interpret this data This gave the group a 95 confidence interval for the proportion of music played per hour that was then used to compare with the random sampling These proportions were as follows Hour 1 81 67 Hour 2 81 67 Hour 3 81 67 Hour 4 76 67 Hour 5 80 00 Hour 6 78 33 This test gave us a 95 confidence interval of 78 to 82 music played per hour on 99 7FM The mean is approximately 80 with a standard deviation of 2 11 For this proc freq analysis the proportions of music versus non music of the instantaneous sampling were compared This test shows that instantaneous random sampling does not give a completely accurate depiction of what is actually being played The continuous sampling test gave us a confidence interval of 78 to 82 music played The instantaneous sampling data provided a 95 exact confidence interval of 55 to 82 These two intervals have the same upper limit but very different lower limits The proportion of music played on 99 7FM in the instantaneous sampling test was only 70 which is outside the 95 confidence interval provided by the continuous sampling interval Therefore the difference is statistically significant and the null hypothesis should be rejected Appendix A Instantaneous Sampling Counts Totals Music 96 5FM 99 7FM Broadcast Type Comm Talk 32 12 6 35 10 5 Raw Data Time 12 04 12 13 12 26 12 31 12 39 12 43 12 44 12 47 12 54 12 59 13 04 13 11 13 18 13 22 13 29 13 37 13 49 13 59 14 13 14 24 14 31 14 45 14 51 14 58 14 59 15 17 15 31 15 33 15 34 15 47 15 51 15 52 15 58 16 07 16 10 16 11 16 25 96 5FM Music Comm Music Music Music Music Talk Comm Music Music Music Music Comm Talk Music Music Music Music Talk Music Music Comm Music Talk Music Music Music Music Music Comm Music Music Talk Music Music Music Music 99 7FM Music Music Talk Talk Music Comm Comm Music Music Talk Music Music Music Comm Music Comm Comm Music Music Music Music Comm Music Music Music Music Comm Music Music Talk Music Music Music Music Comm Music Music 16 29 16 37 16 50 17 05 17 06 17 21 17 23 17 30 17 32 17 37 17 44 17 54 17 57 Music Music Comm Music Music Comm Comm Talk Comm Music Music Comm Comm Music Talk Music Music Music Music Music Music Comm Music Comm Music Music Appendix B Continuous Sampling Totals Legend 1 2 3 4 5 type commerical psa song weather news min 54 19 288 2 5 4 5 363 5 Percent 0 15 0 05 0 78 0 01 0 01 1 00 Raw Data Obs 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Type psa commercial psa song commercial song commercial song commercial song commercial psa commercial weather song commercial song news song Duration 1 1 5 1 5 1 7 4 10 0 5 4 1 1 2 5 0 5 4 0 5 9 1 15 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 psa commercial song commercial song commercial psa commercial weather song news song commercial psa song commercial psa song news song commercial psa song commercial song commercial song commercial song commercial psa song commercial song commercial weather song commercial psa news song commercial song commercial song commercial 1 1 5 4 24 2 1 0 5 0 5 11 1 9 1 4 30 1 5 0 5 11 0 5 8 2 1 5 3 1 8 1 6 1 3 1 5 1 8 2 7 2 0 5 11 2 3 1 14 1 10 2 9 2 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 psa commercial song psa commercial weather song commercial psa commercial news song commerical weather song commercial song 1 3 8 1 2 0 5 7 0 5 2 3 1 13 4 0 5 16 3 13 Appendix C SAS Code Part 1 Instantaneous Random Sampling data intstation input station type count datalines 96 5 M 32 96 5 C 12 96 5 T 6 99 7 M 35 99 7 C 10 99 7 T 5 run proc freq data intstation tables station type chisq weight count run Part 2 Comparisons of Instantaneous and Continuous Sampling options linesize 75 data contstation input hour proportion datalines 1 8167 2 8167 3 8167 4 7667 5 8000 6 7833 run proc means data contstation n mean stddev stderr clm alpha 05 var proportion run data intstation input type count datalines music 35 nonmusic 15 run proc freq data intstation tables type binomial alpha …