An analytics company provided demographic information about US Spotify users. In 2021, it was known that 26% of all US Spotify users were between 18 – 24 years old. All work for this investigation will be completed in StatKey. a) Is the given value of 26% a parameter or a statistic? Answer the question and provide the correct symbol for this value in one sentence. b) Create a sampling distribution of 10,000 samples of sample size 11 for US Spotify users. In StatKey, from the main page, click on Proportion (to the right of sampling distribution). Now do the following: Edit Proportion → Enter 0.26 → Press Ok. Next to ‘Choose samples of size n’, enter 11 and then click ‘Generate 1000 Samples.’ Click ‘Generate 1000 Samples’ nine more times to obtain 10,000 samples in total. Copy your graph (i.e. provide a screenshot) into the solutions document. c) Describe the shape of the sampling distribution in one sentence. d) State the measures of center and spread for your sampling distribution. Provide the names of the measures and the values seen in the top right corner of the image. e) Would it be appropriate to construct a 95% confidence interval with the information in 1(b) through 1(d)? Explain why in one sentence. f) Regardless of your answer in part (e), reset your sampling distribution plot and generate 100 samples of size 11 (keep the proportion set to 0.26). Once you do that, click the Confidence Intervals tab to the right of Data Tables (on the right side of the screen). Take a screenshot of the 100 confidence intervals and paste it into your solutions document. Compare the Coverage percentage to the 95% confidence level in a complete sentence. g) Now we will create a sampling distribution of 10,000 samples of sample size 110. Next to ‘Choose samples of size n’, enter 110 and then click ‘Generate 1000 Samples.’ Click ‘Generate 1000 Samples’ nine more times to obtain 10,000 samples in total. Copy your graph (i.e. provide a screenshot) into the solutions document. h) Describe the shape, center, and spread of the sampling distribution. Make sure to provide the values and names for center and spread in your description. i) Compare the values of center and spread for the sampling distribution generated in part 1(g) to those values found in 1(b) in one to two sentences. Please use the actual values in your comparison. j) Would it be appropriate to construct a 95% confidence interval with the information in 1(g) and 1(h)? Explain why in a complete sentence. k) Regardless of your answer to (j), reset your plot and generate 100 samples of size 110. Once you do that, click the Confidence Intervals tab to the right of Data Tables (on the right side of the screen). Take a screenshot of the 100 confidence intervals and paste it into your solutions document. Compare the Coverage percentage to 95% in a complete sentence. l) Finally, compare the Coverage percentages from (k) and (f) using the actual percentages obtained in your comparisons.
Investigation 1: Age Demographics of Spotify Users
An analytics company provided demographic information about US Spotify users. In 2021, it
was known that 26% of all US Spotify users were between 18 – 24 years old. All work for this
investigation will be completed in StatKey.
a) Is the given value of 26% a parameter or a statistic? Answer the question and provide the
correct symbol for this value in one sentence.
b) Create a sampling distribution of 10,000 samples of
In StatKey, from the main page, click on Proportion (to the right of sampling
distribution). Now do the following: Edit Proportion → Enter 0.26 → Press Ok. Next to
‘Choose samples of size n’, enter 11 and then click ‘Generate 1000 Samples.’ Click
‘Generate 1000 Samples’ nine more times to obtain 10,000 samples in total. Copy your
graph (i.e. provide a screenshot) into the solutions document.
c) Describe the shape of the sampling distribution in one sentence.
d) State the measures of center and spread for your sampling distribution. Provide the names
of the measures and the values seen in the top right corner of the image.
e) Would it be appropriate to construct a 95% confidence interval with the information in
1(b) through 1(d)? Explain why in one sentence.
f) Regardless of your answer in part (e), reset your sampling distribution plot and generate
100 samples of size 11 (keep the proportion set to 0.26). Once you do that, click the
Confidence Intervals tab to the right of Data Tables (on the right side of the screen).
Take a screenshot of the 100 confidence intervals and paste it into your solutions
document. Compare the Coverage percentage to the 95% confidence level in a complete
sentence.
g) Now we will create a sampling distribution of 10,000 samples of sample size 110. Next
to ‘Choose samples of size n’, enter 110 and then click ‘Generate 1000 Samples.’ Click
‘Generate 1000 Samples’ nine more times to obtain 10,000 samples in total. Copy your
graph (i.e. provide a screenshot) into the solutions document.
h) Describe the shape, center, and spread of the sampling distribution. Make sure to provide
the values and names for center and spread in your description.
i) Compare the values of center and spread for the sampling distribution generated in part
1(g) to those values found in 1(b) in one to two sentences. Please use the actual values in
your comparison.
j) Would it be appropriate to construct a 95% confidence interval with the information in
1(g) and 1(h)? Explain why in a complete sentence.
k) Regardless of your answer to (j), reset your plot and generate 100 samples of size 110.
Once you do that, click the Confidence Intervals tab to the right of Data Tables (on the
right side of the screen). Take a screenshot of the 100 confidence intervals and paste it
into your solutions document. Compare the Coverage percentage to 95% in a complete
sentence.
l) Finally, compare the Coverage percentages from (k) and (f) using the actual percentages
obtained in your comparisons.
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