Investigation 1: Appropriateness of Inference For the following scenario, answer the questions below. Please note, do not conduct inference in this problem; just answer each question. Data Set: Track_Name Track_Artist Year Genre Mode Duration Tempo Hells Bells AC/DC 1980 rock Minor 5.204883 106.767 Barbie Girl Aqua 2009 pop Minor 3.250667 129.967 Heat Of The Moment Asia 1982 pop Major 3.793783 136.136 Digital Love Daft Punk 2001 pop Major 5.022883 124.726 Where Them Girls At (feat. Nicki Minaj & Flo Rida) David Guetta 2012 pop Major 3.247333 129.884 Let Me Clear My Throat - Old School Reunion Remix '96 DJ Kool 1996 rap Major 4.836 103.145 Oye Mi Canto - Single Version Gloria Estefan 1989 latin Major 4.12845 119.588 When The Curtain Falls Greta Van Fleet 2018 rap Major 3.716 96.004 Starving Hailee Steinfeld 2016 pop Major 3.031333 99.989 Be My Lover La Bouche 2009 pop Minor 3.995783 134.774 Immigrant Song - Remaster Led Zeppelin 1970 rock Major 2.4375 112.937 Big Fool Levi Belle 2020 r&b Major 3.026917 105.009 Into the Setting Sun Liam Davison 2011 rock Minor 7.645333 85.013 Friedhof der Kuscheltiere Manuellsen 2015 rap Major 2.91845 81.161 One Thing Right - Koni Remix Marshmello 2019 latin Minor 2.4831 105.052 Kids MGMT 2007 rock Major 5.047333 122.961 Sixteen Rick Ross 2012 rap Major 8.25955 86.98 Seasons Shaggy 2017 latin Major 3.23805 97.022 Donde Estas Corazon Shakira 1995 latin Major 3.86155 109.044 Just Got Paid ZZ Top 1972 rock Major 4.458 99.93 A researcher wanted to use a random sample of 20 Spotify Songs to estimate the average Duration (in minutes) and average Tempo (in bpm) for the population of all songs on Spotify. The researcher does not have any additional information about the population of all Spotify Songs. The data set is called SongSample1. a) Based on the above scenario, which method of statistical inference do you believe the researcher will consider to complete this estimation? Answer this question in one sentence and provide a reason for your choice. b) If we attempt to conduct statistical inference using the collected sample, what are the two parameters of interest to the researcher? Use the correct symbols and describe the parameters in context in one sentence each. c) Check the following conditions necessary to consider conducting inference using theorybased methods and the t-distribution. There are three to consider: (1) Was a random sample collected; (2) Is the population where the sample comes from normal; and (3) Is the sample size greater than or equal to 30? Check each of these conditions in one sentence. d) For the Duration variable, construct a frequency histogram in Rguroo. Remember to properly title and label the graph. Copy and paste this graph into your document. e) Describe the shape of the Duration histogram in one sentence. f) For the Duration variable, construct one horizontal boxplots in Rguroo. Remember to properly title and label the graph. Copy and paste this graph into your document. g) Does the Duration boxplot show any outliers? Answer this question in one sentence and identify any outliers if they are present. h) For the Tempo variable, construct a frequency histogram in Rguroo. Remember to properly title and label the graph. Copy and paste this graph into your document. i) Describe the shape of the Tempo histogram in one sentence. j) For the Tempo variable, construct one horizontal boxplots in Rguroo. Remember to properly title and label the graph. Copy and paste this graph into your document. k) Does the Tempo boxplot show any outliers? Answer this question in one sentence and identify any outliers if they are present. l) Considering your interpretation of each variable’s graphs, is theory-based inference using the t-distribution appropriate for either variable (or both variables, or neither variable)? Answer the question and provide a reason for your response. m) If theory-based inference is not appropriate for one or both of the variables, present another possibility if the researcher still wanted to conduct statistical inference. Use one to three complete sentences in your response.