A random survey of enrollment at 2020 community colleges across the United States yielded the following figures: 21,84621,846; 2,0922,092; 9,4149,414; 7,6817,681; 3,2003,200; 17,50017,500; 9,2009,200; 7,3807,380; 18,31418,314; 6,5576,557; 13,71313,713; 17,76817,768; 7,4937,493; 2,7712,771; 2,8612,861; 1,2631,263; 7,2857,285; 28,16528,165; 5,0805,080; 11,68911,689. (a) Assume the underlying population is normal. i. xˉ=x‾= ii. sx=sx= iii. n=n= iv. n−1=n−1= (b) Define the random variables XX and XˉX‾ in words XX is the number of students enrolled at a community college in the United States. XˉX‾ is the mean number of students enrolled from a sample of 2020 community colleges in the United States. XX is the number of students enrolled at a community college in the United States. XˉX‾ is the number of students enrolled from a sample of 2020 community colleges in the United States. XX is the mean number of students enrolled from a sample of 2020 community colleges in the United States. XˉX‾ is the number of students enrolled at a community college in the United States. XX is the number of students enrolled from a sample of 2020 community colleges in the United States. XˉX‾ is the mean number of students enrolled in a community college in the United States. XX is the number of students enrolled at a community college in the United States. XˉX‾ is the mean number of students enrolled from the population of community colleges in the United States. (c) Which distribution should you use for this problem? Explain your choice. Xˉ∼t20X‾∼t20, since the sample size is small σσ is being used as an estimate for ss. Xˉ∼t19X‾∼t19, since the sample size is small σσ is being used as an estimate for ss. Xˉ∼t20X‾∼t20, since the sample size is small and ss is being used as an estimate for σσ. Xˉ∼N(10,064,7,341)X‾∼N10,064,7,341, since the underlying population is normal. Xˉ∼t19X‾∼t19, since the sample size is small and ss is being used as an estimate for σσ. (d) Construct a 97%97% confidence interval for the population mean enrollment at community colleges in the United States. Enter your answer in interval notation. Round your answer to the nearest integer. Do not round any intermediate calculations. (e) What will happen to the error bound and confidence interval if 55 community colleges were surveyed? Why? The error bound and confidence interval will both increase since decreasing the sample size decreases variability in the sample. The error bound and confidence interval will both decrease since decreasing the sample size decreases variability in the sample. The error bound and confidence interval will both increase since decreasing the sample size increases variability in the sample. The error bound and confidence interval will both decrease since decreasing the sample size increases variability in the sample.
A random survey of enrollment at 2020 community colleges across the United States yielded the following figures:
21,84621,846; 2,0922,092; 9,4149,414; 7,6817,681; 3,2003,200; 17,50017,500; 9,2009,200; 7,3807,380; 18,31418,314; 6,5576,557; 13,71313,713; 17,76817,768; 7,4937,493; 2,7712,771; 2,8612,861; 1,2631,263; 7,2857,285; 28,16528,165; 5,0805,080; 11,68911,689.
(a) Assume the underlying population is normal.
i.
xˉ=x‾=
ii.
sx=sx=
iii.
n=n=
iv.
n−1=n−1=
(b) Define the random variables XX and XˉX‾ in words
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XX is the number of students enrolled at a community college in the United States. XˉX‾ is the mean number of students enrolled from a sample of 2020 community colleges in the United States. |
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XX is the number of students enrolled at a community college in the United States. XˉX‾ is the number of students enrolled from a sample of 2020 community colleges in the United States. |
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XX is the mean number of students enrolled from a sample of 2020 community colleges in the United States. XˉX‾ is the number of students enrolled at a community college in the United States. |
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XX is the number of students enrolled from a sample of 2020 community colleges in the United States. XˉX‾ is the mean number of students enrolled in a community college in the United States. |
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XX is the number of students enrolled at a community college in the United States. XˉX‾ is the mean number of students enrolled from the population of community colleges in the United States. |
(c) Which distribution should you use for this problem? Explain your choice.
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Xˉ∼t20X‾∼t20, since the |
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Xˉ∼t19X‾∼t19, since the sample size is small σσ is being used as an estimate for ss. |
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Xˉ∼t20X‾∼t20, since the sample size is small and ss is being used as an estimate for σσ. |
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Xˉ∼N(10,064,7,341)X‾∼N10,064,7,341, since the underlying population is normal. |
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Xˉ∼t19X‾∼t19, since the sample size is small and ss is being used as an estimate for σσ. |
(d) Construct a 97%97% confidence interval for the population mean enrollment at community colleges in the United States.
Enter your answer in interval notation.
Round your answer to the nearest integer.
Do not round any intermediate calculations.
(e) What will happen to the error bound and confidence interval if 55 community colleges were surveyed? Why?
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The error bound and confidence interval will both increase since decreasing the sample size decreases variability in the sample. |
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The error bound and confidence interval will both decrease since decreasing the sample size decreases variability in the sample. |
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The error bound and confidence interval will both increase since decreasing the sample size increases variability in the sample. |
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The error bound and confidence interval will both decrease since decreasing the sample size increases variability in the sample. |
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