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A music fan claims that R&B songs tend to have a more positive tone on average than do Rap songs. The individual collected two independent random samples from the population of Spotify Songs. Fifteen R&B songs and another fifteen Rap songs were collected and their Valence was recorded. The music fan believed that pairing the song by their Danceability may provide additional information. Danceability describes how suitable a track is for dancing based on a combination of musical elements including tempo, rhythm stability, beat strength, and overall regularity. A value of 0.0 is least danceable and 1 is most danceable. Thus, the individual paired the 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&B song 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, assume

A music fan claims that R&B songs tend to have a more positive tone on average than do Rap songs. The individual collected two independent random samples from the population of Spotify Songs. Fifteen R&B songs and another fifteen Rap songs were collected and their Valence was recorded. The music fan believed that pairing the song by their Danceability may provide additional information. Danceability describes how suitable a track is for dancing based on a combination of musical elements including tempo, rhythm stability, beat strength, and overall regularity. A value of 0.0 is least danceable and 1 is most danceable. Thus, the individual paired the 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&B song 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, assume

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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RBValence RapValence RBDance RapDance
0.397 0.24 0.311 0.337
0.383 0.205 0.32 0.401
0.264 0.26 0.383 0.437
0.46 0.338 0.395 0.465
0.449 0.54 0.401 0.468
0.436 0.0371 0.407 0.482
0.516 0.217 0.521 0.487
0.381 0.499 0.548 0.506
0.53 0.577 0.594 0.547
0.631 0.684 0.635 0.552
0.714 0.78 0.706 0.57
0.799 0.463 0.72 0.598
0.64 0.547 0.727 0.778
0.902 0.826 0.866 0.884
0.845 0.847 0.896 0.906
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 Rap songs. The individual collected two independent random samples from the population of Spotify Songs. Fifteen R&B songs and another fifteen Rap songs were collected and their Valence was recorded. The music fan believed that pairing the song by their Danceability may provide additional information. Danceability describes how suitable a track is for dancing based on a combination of musical elements including tempo, rhythm stability, beat strength, and overall regularity. A value of 0.0 is least danceable and 1 is most danceable. Thus, the individual paired the 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&B song 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, assume the Central Limit Theorem conditions hold. The data set is called RBRapSample32. The data set includes columns for each genre's valence and 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 this pairing method was chosen? Answer this question using one complete sentence. b) Define the population parameter for this investigation in context and symbols in one sentence. c) State the null and alternative hypothesis to test the claim that a difference exists in the mean Valence between R&B and Rap songs using correct notation Please consider the new data design. d) Again, we will obtain a 90% confidence interval to make the hypothesis test decision by following these directions. ● ● ● ● In Rguroo, go to Analytics → Analysis → Mean Inference → One & Two Populations. In the Dataset dropdown, select RBRapSample32. In the Variable 1 dropdown, select RBValence. Variable 2 dropdown, select Rap 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 Interval tab is selected. Change the Confidence level to 0.90. Then, select t-statistic under Method. 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 state the confidence interval. e) Make a decision whether or not to reject the null hypothesis using the confidence interval by checking to see if the null value is captured by the confidence interval. State the decision and explanation in one sentence.
Transcribed Image Text: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 Rap songs. The individual collected two independent random samples from the population of Spotify Songs. Fifteen R&B songs and another fifteen Rap songs were collected and their Valence was recorded. The music fan believed that pairing the song by their Danceability may provide additional information. Danceability describes how suitable a track is for dancing based on a combination of musical elements including tempo, rhythm stability, beat strength, and overall regularity. A value of 0.0 is least danceable and 1 is most danceable. Thus, the individual paired the 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&B song 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, assume the Central Limit Theorem conditions hold. The data set is called RBRapSample32. The data set includes columns for each genre's valence and 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 this pairing method was chosen? Answer this question using one complete sentence. b) Define the population parameter for this investigation in context and symbols in one sentence. c) State the null and alternative hypothesis to test the claim that a difference exists in the mean Valence between R&B and Rap songs using correct notation Please consider the new data design. d) Again, we will obtain a 90% confidence interval to make the hypothesis test decision by following these directions. ● ● ● ● In Rguroo, go to Analytics → Analysis → Mean Inference → One & Two Populations. In the Dataset dropdown, select RBRapSample32. In the Variable 1 dropdown, select RBValence. Variable 2 dropdown, select Rap 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 Interval tab is selected. Change the Confidence level to 0.90. Then, select t-statistic under Method. 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 state the confidence interval. e) Make a decision whether or not to reject the null hypothesis using the confidence interval by checking to see if the null value is captured by the confidence interval. State the decision 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 the directions 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 your decision 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 you believe 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 question in one sentence and please provide a reason for your answer. j) Can we determine if a cause and effect relationship exists between the variables? Answer this question in one sentence and please provide a reason for your answer.
Transcribed Image Text: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 the directions 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 your decision 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 you believe 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 question in one sentence and please provide a reason for your answer. j) Can we determine if a cause and effect relationship exists between the variables? Answer this question in one sentence and please provide a reason for your answer.
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