In this investigation, we would like to know if Spotify songs from the decade of the 1980s have an average duration longer than 4.4 minutes. From our original Spotify sample, a subset was generated containing all songs from the 1980s. The data set is called 80sSubset and is posted on blackboard.
Investigation 3: Duration of Songs from the 1980s
In this investigation, we would like to know if Spotify songs from the decade of the 1980s have
an average duration longer than 4.4 minutes. From our original Spotify sample, a subset was
generated containing all songs from the 1980s. The data set is called 80sSubset and is posted on
blackboard.
a) Define the parameter of interest in context using symbol(s) and words in one complete
sentence.
b) State the null and alternative hypotheses using correct notation.
c) Obtain the observed statistic from the 80sSubset we will use to complete this test. Use
Analytics → Analysis → Numerical Summaries. Select the 80sSubset in the “Select a
Dataset” menu and then select Duration as the variable. Then click Univariate and select
the correct statistic. Screenshot the table and paste it into your solutions document.
d) Create a randomization distribution by following these instructions. In StatKey, go to the
right pane labeled ‘Randomization Hypothesis Tests’ and click Test for Single Mean.
Upload the file in ‘Upload File’ or manually edit the column of data in ‘Edit Data.’
Change the ‘Null hypothesis: µ’ to the mean you stated in your null hypothesis. Next,
click ‘Generate 1000 Samples’ 10 times to generate 10,000 samples. Screenshot your
entire randomization distribution and paste it into your solutions document.
e) Describe the shape of the distribution. Based on your answer, are we able to continue
with a randomized hypothesis test? Answer in one sentence.
f) Regardless of your answer in 3(e), calculate the p-value of this test. To find the p-value
from the randomization distribution click either ‘Left Tail’, ‘Two-Tail’, or ‘Right Tail’ in
the top left corner of the graph based on your alternative hypothesis. Then, change the
bottom blue box(es) to the sample mean we observed. Provide a screenshot of the image
you built to obtain the p-value and state the p-value below the image.
g) Explain what this p-value means in context of the question in one sentence.
h) State whether you reject or do not reject the null hypothesis and a reason for your
decision in one sentence.
i) Based on the above decision, state your conclusion addressing the research question, in
context in one sentence.
j) Based on your decision, what kind of error could you have made, and explain what that
would mean in the context of the problem? Answer the question in one sentence.
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