A random survey of enrollment at 2020 community colleges across the United States yielded the following figures:21,845; 2,442; 9,414; 7,681; 3,200; 17,500; 9,200; 7,380; 18,314; 6,557; 13,713; 17,768; 7,493; 2,771; 2,861; 1,263; 7,285; 28,165; 5,080; 11,658(a) Assume the underlying population is normal.i. x‾=ii. sx= iii. n= iv. n−1= (d) Construct a 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. (b) Define the random variables X and X in wordsX is the number of students enrolled from a sample of 20 community colleges in the United States. X isthe mean number of students enrolled in a community college in the United States.X is the number of students enrolled at a community college in the United States. X is the mean numberof students enrolled from a sample of 20 community colleges in the United States.X is the number of students enrolled at a community college in the United States. X is the mean numberof students enrolled from the population of community colleges in the United States.X is the mean number of students enrolled from a sample of 20 community colleges in the United States.X is the number of students enrolled at a community college in the United States.X is the number of students enrolled at a community college in the United States. X is the number ofstudents enrolled from a sample of 20 community colleges in the United States.(c) Which distribution should you use for this problem? Explain your choice.o X~ t20, since the sample size is small o is being used as an estimate for s.o X~ t19, since the sample size is small and s is being used as an estimate for o.o X~ t19. since the sample size is small o is being used as an estimate for s.o X~ t20, since the sample size is small and s is being used as an estimate for o.o X~ N (10,070, 7,332), since the underlying population is normal. (e) What will happen to the error bound and confidence interval if 300 community colleges were surveyed?Why?The error bound and confidence interval will both increase since increasing the sample size decreasesvariability in the sample.The error bound and confidence interval will both increase since increasing the sample size increasesvariability in the sample.The error bound and confidence interval will both decrease since increasing the sample size increasesvariability in the sample.The error bound and confidence interval will both decrease since increasing the sample size decreasesvariability in the sample.

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Answered: A random survey of enrollment at 2020…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A random survey of enrollment at 2020 community colleges across the United States yielded the following figures:

21,845; 2,442; 9,414; 7,681; 3,200; 17,500; 9,200; 7,380; 18,314; 6,557; 13,713; 17,768; 7,493; 2,771; 2,861; 1,263; 7,285; 28,165; 5,080; 11,658

(a) Assume the underlying population is normal.

i. x‾=

ii. sx=

iii. n=

iv. n−1=

(d) Construct a 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.

(b) Define the random variables X and X in words
X is the number of students enrolled from a sample of 20 community colleges in the United States. X is
the mean number of students enrolled in a community college in the United States.
X is the number of students enrolled at a community college in the United States. X is the mean number
of students enrolled from a sample of 20 community colleges in the United States.
X is the number of students enrolled at a community college in the United States. X is the mean number
of students enrolled from the population of community colleges in the United States.
X is the mean number of students enrolled from a sample of 20 community colleges in the United States.
X is the number of students enrolled at a community college in the United States.
X is the number of students enrolled at a community college in the United States. X is the number of
students enrolled from a sample of 20 community colleges in the United States.
(c) Which distribution should you use for this problem? Explain your choice.
o X~ t20, since the sample size is small o is being used as an estimate for s.
o X~ t19, since the sample size is small and s is being used as an estimate for o.
o X~ t19. since the sample size is small o is being used as an estimate for s.
o X~ t20, since the sample size is small and s is being used as an estimate for o.
o X~ N (10,070, 7,332), since the underlying population is normal.

(e) What will happen to the error bound and confidence interval if 300 community colleges were surveyed?
Why?
The error bound and confidence interval will both increase since increasing the sample size decreases
variability in the sample.
The error bound and confidence interval will both increase since increasing the sample size increases
variability in the sample.
The error bound and confidence interval will both decrease since increasing the sample size increases
variability in the sample.
The error bound and confidence interval will both decrease since increasing the sample size decreases
variability in the sample.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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