Question
A random survey of enrollment at2020community colleges across the United States yielded the following figures: 21,83821,838; 2,1122,112;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;11,76211,762. (a) Assume the underlying population is normal. i.
A random survey of enrollment at2020community colleges across the United States yielded the following figures:
21,83821,838; 2,1122,112;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;11,76211,762.
(a) Assume the underlying population is normal.
i.
x=x=
ii.
sx=sx=
iii.
n=n=
iv.
n1=n1=
(b) Define the random variablesXXandXXin words
XXis the number of students enrolled at a community college in the United States.XXis the number of students enrolled from a sample of2020community colleges in the United States. | ||
XXis the mean number of students enrolled from a sample of2020community colleges in the United States.XXis the number of students enrolled at a community college in the United States. | ||
XXis the number of students enrolled from a sampleof2020community colleges in the United States.XXis the mean number of students enrolled in a community college in the United States. | ||
XXis the number of students enrolled at a community college in the United States.XXis the mean number of students enrolled from a sample of2020community colleges in the United States. | ||
XXis the number of students enrolled at a community college in the United States.XXis 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.
XN(10,068,7,340)XN10,068,7,340, since the underlying population is normal. | ||
Xt20Xt20, sincethe sample size is smallis being used as an estimate forss. | ||
Xt20Xt20, since the sample size is small andssis being used as an estimate for. | ||
Xt19Xt19, since the sample size is small andssis being used as an estimate for. | ||
Xt19Xt19, sincethe sample size is smallis being used as an estimate forss. |
(d) Construct a98%98%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 if1717community 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 decrease since decreasing the sample size increases variability in the sample. | ||
The error bound and confidence interval will both increase since decreasing the sample size increases variability in the sample. |
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Mathematical Statistics With Applications In R
Authors: Chris P. Tsokos, K.M. Ramachandran
2nd Edition
124171133, 978-0124171138
