Investigation 4: Tempo Differences Between Genres Now we will consider if the difference in the mean tempos between the genres EDM (electronic dance music) and rock is significant. The data set is provided on the blackboard as a .csv file called Tempo4. We are subtracting (EDM – rock) when calculating the difference. Total of EDM Songs: 640 Total of Rock Songs: 512 a) Obtain the value of the observed statistic used to estimate the parameter using StatKey or Rguroo. Upload your data set to either program to obtain your statistic and state the statistic rounded to one decimal place as your answer to this part. b) Define the parameter of interest in context using the symbol(s) and words in one sentence. c) State the null and alternative hypotheses using correct notation. d) Create a bootstrap distribution by following these instructions. In StatKey, go to the middle pane labeled ‘Bootstrap Confidence Interval’ and click CI for Difference in Means. Upload the file in ‘Upload File’ or manually edit the data in ‘Edit Data.’ Click ‘Generate 1000 Samples.’ Click this button nine more times to obtain 10,000 samples in total. Copy or screenshot your distribution (which must display the number of samples, the mean, and the std. error) in your solutions document. e) Construct a 99% confidence interval using percentiles. Go to the top left corner of the distribution and click ‘Two-Tail’ and then enter the percentile values needed based on the significance level. Copy your distribution that must display the confidence interval values (all five blue boxes) into your solutions document. Also, provide your confidence interval in the format (lower value, upper value). f) Based on the confidence interval, provide a decision for the hypothesis test and explain your reasoning in one or two sentences. g) If we changed the significance level to 0.05 and constructed a 95% confidence interval, what would happen to the width confidence interval? In addition, explain if your decision from 4(f) changes if the significance level changes to 0.05. h) Create a randomization distribution by following these instructions. In StatKey, go to the right pane labeled ‘Randomization Hypothesis Tests’ and click ‘Test for Difference in Means.’ Upload the file in ‘Upload File’ or manually edit the data in ‘Edit Data.’ Click ‘Generate 1000 Samples.’ Click this button nine more times to generate 10,000 samples in total. Take a screenshot of your randomization distribution (which must display the number of samples, the mean, and the std. error) and paste it into your solutions document. i) Calculate the p-value from your randomization distribution using your observed statistic calculated in part (a). First, click the ‘Right Tail’ button and enter the value of your observed statistic in the blue box below the x-axis. Next, click the ‘Left Tail’ button and enter the negative value of your observed statistic in the blue box below the x-axis (to the left of zero). Then, if necessary, readjust your bottom blue box to the right of zero to correctly display the value
Investigation 4: Tempo Differences Between Genres
Now we will consider if the difference in the
dance music) and rock is significant. The data set is provided on the blackboard as a .csv file called
Tempo4. We are subtracting (EDM – rock) when calculating the difference.
Total of EDM Songs: 640 Total of Rock Songs: 512
a) Obtain the value of the observed statistic used to estimate the parameter using StatKey or
Rguroo. Upload your data set to either program to obtain your statistic and state the
statistic rounded to one decimal place as your answer to this part.
b) Define the parameter of interest in context using the symbol(s) and words in one sentence.
c) State the null and alternative hypotheses using correct notation.
d) Create a bootstrap distribution by following these instructions. In StatKey, go to the
middle pane labeled ‘Bootstrap Confidence Interval’ and click CI for Difference in
Means. Upload the file in ‘Upload File’ or manually edit the data in ‘Edit Data.’ Click
‘Generate 1000 Samples.’ Click this button nine more times to obtain 10,000 samples in
total. Copy or screenshot your distribution (which must display the number of samples,
the mean, and the std. error) in your solutions document.
e) Construct a 99% confidence interval using percentiles. Go to the top left corner of the
distribution and click ‘Two-Tail’ and then enter the percentile values needed based on
the significance level. Copy your distribution that must display the confidence interval
values (all five blue boxes) into your solutions document. Also, provide your confidence
interval in the format (lower value, upper value).
f) Based on the confidence interval, provide a decision for the hypothesis test and explain
your reasoning in one or two sentences.
g) If we changed the significance level to 0.05 and constructed a 95% confidence interval,
what would happen to the width confidence interval? In addition, explain if your
decision from 4(f) changes if the significance level changes to 0.05.
h) Create a randomization distribution by following these instructions. In StatKey, go to the
right pane labeled ‘Randomization Hypothesis Tests’ and click ‘Test for Difference in
Means.’ Upload the file in ‘Upload File’ or manually edit the data in ‘Edit Data.’ Click
‘Generate 1000 Samples.’ Click this button nine more times to generate 10,000 samples
in total. Take a screenshot of your randomization distribution (which must display the
number of samples, the mean, and the std. error) and paste it into your solutions
document.
i) Calculate the p-value from your randomization distribution using your observed statistic
calculated in part (a). First, click the ‘Right Tail’ button and enter the value of your
observed statistic in the blue box below the x-axis. Next, click the ‘Left Tail’ button and
enter the negative value of your observed statistic in the blue box below the x-axis (to the
left of zero). Then, if necessary, readjust your bottom blue box to the right of zero to
correctly display the value of the observed statistic. Copy the distribution image
including the five blue boxes into your document. Finally, add the values of the two blue
boxes above their corresponding red x’s to obtain the p-value.
j) Using a significance level of 0.05 and based on the p-value found in 4(i), state whether
you reject or do not reject the null hypothesis and a reason for your decision in one
sentence.
k) Based on the above decision, state your conclusion addressing the research question, in
the context in a complete sentence.
l) Using a significance level of 0.01 and based on the p-value found in 4(i), state whether
you reject or do not reject the null hypothesis and a reason for your decision in one
sentence.
m) Based on the above decisions, state your conclusion addressing the research question, in
the context in a complete sentence.
n) In general, explain how the bootstrap confidence interval and the randomization
hypothesis test relate to one another in one to two sentences.
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