Investigation 2: Songs from Spotify – Mode and Popularity A random sample of 3439 songs was selected from the Spotify database and twelve variables were measured for each song. Remember, the Mode variable indicates the type of scale the song’s melodic content is derived from (Major or Minor). Popularity is on a scale of 0 to 100 and songs with higher numbers are more popular. Let us now investigate whether Major songs are significantly more “Popular” than Minor songs. Let us define “Popular” as songs that earned a popularity rating of 50 or higher. From the random sample of songs, there were 1964 Major songs and of those 853 were rated “Popular.” In addition, there were 1475 Minor songs and of those 587 were rated “Popular.” In this investigation we will subtract (Major – Minor) a) Define the population parameter using context and symbols in one complete sentence. b) State the hypotheses using the claim. c) Check the specific conditions necessary to consider conducting inference using theorybased (or distribution based) methods. There are two to consider: (1) Was the data collected randomly from the population; and (2) Are there at least ten successes and failures in each group? Answer each of these questions in one sentence and show that condition (2) is true or false using calculation to obtain the failures (note the successes are given). d) Calculate and label the two sample proportions separately and round the values to four decimal places. Next, calculate the difference between these sample proportions by subtracting (Major – Minor). Type all of these calculations and label each of them. e) Calculate the pooled proportion estimate needed in the calculation of the standard error of the test statistic. Type this calculation and round to four decimal places. f) Calculate the test statistic value using your proportions obtained in parts (d) and (e) and type your work. Round your test statistic value to two decimal places. g) Obtain your p-value using your test statistic calculated in part (f) in StatKey using Theoretical Distributions → Normal. Copy and paste the image of the standard normal distribution with all blue boxes displayed and type the value of the p-value below the image. h) Verify your test statistic and p-value using Rguroo. Go to Analytics → Analysis → Proportion Inference → Two Populations. See the image below to fill in each box correctly. Then, click the Test of Hypothesis tab and choose Large Sample z under method. Finally, correctly set your alternative hypothesis and significance level to = 0.01 and click Preview. Copy and paste only the output and table displayed under the title “Two Population Proportion Test of Hypothesis” i) Based on your p-value, make a decision using = 0.01 to either reject or not reject the null hypothesis. Be sure to show the comparison of the p-value to the significance level. j) Draw a conclusion based on your decision from part (i) by answering the initial question posed by the political scientist in one or two complete sentences. k) Would your decision and conclusion change if the significance level was 0.05 instead of 0.01? Make a decision and draw your conclusion using = 0.05 instead of = 0.01 using two or three sentences.
Investigation 2: Songs from Spotify –
A random sample of 3439 songs was selected from the Spotify database and twelve variables
were measured for each song. Remember, the Mode variable indicates the type of scale the
song’s melodic content is derived from (Major or Minor). Popularity is on a scale of 0 to 100
and songs with higher numbers are more popular. Let us now investigate whether Major songs
are significantly more “Popular” than Minor songs. Let us define “Popular” as songs that
earned a popularity rating of 50 or higher. From the random sample of songs, there were 1964
Major songs and of those 853 were rated “Popular.” In addition, there were 1475 Minor songs
and of those 587 were rated “Popular.” In this investigation we will subtract (Major – Minor)
a) Define the population parameter using context and symbols in one complete sentence.
b) State the hypotheses using the claim.
c) Check the specific conditions necessary to consider conducting inference using theorybased (or distribution based) methods. There are two to consider: (1) Was the data
collected randomly from the population; and (2) Are there at least ten successes and
failures in each group? Answer each of these questions in one sentence and show that
condition (2) is true or false using calculation to obtain the failures (note the successes
are given).
d) Calculate and label the two sample proportions separately and round the values to four
decimal places. Next, calculate the difference between these sample proportions by
subtracting (Major – Minor). Type all of these calculations and label each of them.
e) Calculate the pooled proportion estimate needed in the calculation of the standard error of
the test statistic. Type this calculation and round to four decimal places.
f) Calculate the test statistic value using your proportions obtained in parts (d) and (e) and
type your work. Round your test statistic value to two decimal places.
g) Obtain your p-value using your test statistic calculated in part (f) in StatKey using
Theoretical Distributions → Normal. Copy and paste the image of the standard normal
distribution with all blue boxes displayed and type the value of the p-value below the
image.
h) Verify your test statistic and p-value using Rguroo. Go to Analytics → Analysis →
Proportion Inference → Two Populations. See the image below to fill in each box
correctly. Then, click the Test of Hypothesis tab and choose Large Sample z under
method. Finally, correctly set your alternative hypothesis and significance level to =
0.01 and click Preview. Copy and paste only the output and table displayed under the
title “Two Population Proportion Test of Hypothesis”
i) Based on your p-value, make a decision using = 0.01 to either reject or not reject the
null hypothesis. Be sure to show the comparison of the p-value to the significance level.
j) Draw a conclusion based on your decision from part (i) by answering the initial question
posed by the political scientist in one or two complete sentences.
k) Would your decision and conclusion change if the significance level was 0.05 instead of
0.01? Make a decision and draw your conclusion using = 0.05 instead of = 0.01
using two or three sentences.
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