Exercise sheet 7 1. It is a well-known phenomenon that radio stations in the USA prefer to play songs that are shorter t

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Exercise Sheet 7 1 It Is A Well Known Phenomenon That Radio Stations In The Usa Prefer To Play Songs That Are Shorter T 1 (181.16 KiB) Viewed 27 times

Exercise sheet 7 1. It is a well-known phenomenon that radio stations in the USA prefer to play songs that are shorter than 3 minutes (180 seconds). This motivates some artists (not all) to write shorter songs in order to get a spot on the show. The following dataset summarizes the lengths (in seconds) of 6 songs of the American band Nirvana: Name Length 1 School 2 Sifting 3 Smells Like Teen Spirit 4 Heart-Shaped Box 5 Swap Meet 6 Pennyroyal Tea 162 322 301 281 183 217 Can you see such a trend for the band Nirvana? To answer the question decide which of the fol- lowing statements are true. The following test results could be helpful, where in the proportion test a duration greater than 180 was rated as 'success'. Asymptotic binomial test data: 5 and 6 Z = 1.633, p-value = 0.9488 alternative hypothesis: true probability of success is less than 0.5 95 percent confidence interval: 0.00000 1.08359 sample estimates: probability of success 0.8333333 One Sample t-test data: Length t = 2.3824, df = 5, p-value = 0.9685 alternative hypothesis: true mean is less than 180 95 percent confidence interval: -Inf 298.7463 sample estimates: mean of x 244.3333 True or false? Justify your answer! a) In order to perform the proportion test, one must first convert the given metric variable into a categorical one. b) The first R output fits the hypotheses: Hou < 180, HA: > 180. c) The second R output fits the hypotheses: H. : 0 > 0.5, HA: 0 <0.5. d) When comparing the p-value of the first test result with 0.05, one can directly (without further calculations) make a decision about the validity of the following statement: "It can be shown that more than half of the songs of Nirvana are longer than 180 seconds." (significance level 0.05) Summer term 2022 Methodology 2: Statistics >> e) When comparing the p-value of the first test result with 0.05, one can directly (without further calculations) make a decision about the validity of the following statement: "It can be shown that more than half of the songs of Nirvana are shorter than 180 seconds." (significance level 0.05) f) Both test results reject the null hypothesis. (significance level 0.05)