RBValenceRapValenceRBDanceRapDance0.3970.240.3110.3370.3830.2050.320.4010.2640.260.3830.4370.460.3380.3950.4650.4490.540.4010.4680.4360.03710.4070.4820.5160.2170.5210.4870.3810.4990.5480.5060.530.5770.5940.5470.6310.6840.6350.5520.7140.780.7060.570.7990.4630.720.5980.640.5470.7270.7780.9020.8260.8660.8840.8450.8470.8960.906 Investigation 3.2: Valence Differences Between R&B and Rap Genres (Paired)A music fan claims that R&B songs tend to have a more positive tone on average than do Rapsongs. The individual collected two independent random samples from the population of SpotifySongs. Fifteen R&B songs and another fifteen Rap songs were collected and their Valence wasrecorded. The music fan believed that pairing the song by their Danceability may provideadditional information. Danceability describes how suitable a track is for dancing based on acombination of musical elements including tempo, rhythm stability, beat strength, and overallregularity. A value of 0.0 is least danceable and 1 is most danceable. Thus, the individual pairedthe R&B song with the lowest danceability with the Rap song with the lowest danceability,followed by the second and second, third and third. She continued this process until the R&Bsong with the highest danceability was paired with the Rap song with the highest danceability,We will continue to subtract (R&B – Rap) and use the 10% significance level. Again, assumethe Central Limit Theorem conditions hold.The data set is called RBRapSample32. The data set includes columns for each genre's valenceand danceability. Again, assume the Central Limit Theorem conditions hold.a) What specific method of pairing was used in this problem and why do you think thispairing method was chosen? Answer this question using one complete sentence.b) Define the population parameter for this investigation in context and symbols in onesentence.c) State the null and alternative hypothesis to test the claim that a difference exists in themean Valence between R&B and Rap songs using correct notation Please consider thenew data design.d) Again, we will obtain a 90% confidence interval to make the hypothesis test decision byfollowing these directions.●●●●In Rguroo, go to Analytics → Analysis → Mean Inference → One & TwoPopulations.In the Dataset dropdown, select RBRapSample32.In the Variable 1 dropdown, select RBValence. Variable 2 dropdown, selectRap Valence.Under the Summary tab, check the box to the left of Paired Data.Next, select the fourth tab Population 1-2 and note that the Confidence Intervaltab is selected. Change the Confidence level to 0.90. Then, select t-statistic underMethod. Leave the Assumptions box on the right as is and click Preview.Provide either a screenshot or a copy of your confidence interval output table and statethe confidence interval.e) Make a decision whether or not to reject the null hypothesis using the confidence intervalby checking to see if the null value is captured by the confidence interval. State thedecision and explanation in one sentence. f) Draw a conclusion about the claim using one or two sentences in context of the problem.g) Verify your decision by obtaining a test statistic and p-value in Rguroo. Follow thedirections presented in part (d). Now, select the Test of Hypothesis tab. In this tab,change the significance level to 0.10 and update the alternative hypothesis. Select t-statistic under Method. Leave the Assumptions box on the right as is. Click Preview.Provide either a screenshot or a copy of your hypothesis test output table and verify yourdecision by comparing your p-value to the significance level in one complete sentence.h) Compare the values of the standard errors calculated in 3.1(c) and 3.2(d). Why do youbelieve these standard errors differ? Answer these questions in one or two sentences.i) Can we generalize these results to a larger group (i.e. a population)? Answer this questionin one sentence and please provide a reason for your answer.j) Can we determine if a cause and effect relationship exists between the variables? Answerthis question in one sentence and please provide a reason for your answer.

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6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P