The following table shows the number of active military personnel in 2009, by region (including the District of Columbia).Pacific229,634Mountain89,816West South Central177,336West North Central64,564East North Central26,384East South Central68,440South Atlantic376,034Middle Atlantic41,441New England8,579Source: U.S. Census Bureau, Statistical Abstract of the United States: 2012, Table 508 (data) and U.S. Census Bureau, Census Regions and Divisions of the United States (regions).Calculate the mean and standard deviation for the population.Now take 10 samples of size 3 from the population. Use either simple random sampling or systematic sampling with the help of the table of random numbers in Appendix A. Calculate the mean for each sample.Once you have calculated the mean for each sample, calculate the mean of means (i.e., add up your 10 sample means and divide by 10). How does this mean compare with the mean for all states?How does the value of the standard deviation that you calculated in Exercise 8a compare with the value of the standard error (i.e., the standard deviation of the sampling distribution)?Construct two histograms, one for the distribution of values in the population and the other for the various sample means taken from Exercise 8b. Describe and explain any differences you observe between the two distributions.It is important that you have a clear sense of the population that we are working with in this exercise. What is the population?

Given Information: Pacific 229,634 Mountain 89,816 West South Central 177,336 West…

Answered: The following table shows the number of…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter9: Sequences, Probability And Counting Theory

Section9.5: Counting Principles

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The following table shows the number of active military personnel in 2009, by region (including the District of Columbia).

Pacific	229,634	Mountain	89,816	West South Central	177,336
West North Central	64,564	East North Central	26,384	East South Central	68,440
South Atlantic	376,034	Middle Atlantic	41,441	New England	8,579

Source: U.S. Census Bureau, Statistical Abstract of the United States: 2012, Table 508 (data) and U.S. Census Bureau, Census Regions and Divisions of the United States (regions).

Calculate the mean and standard deviation for the population.
Now take 10 samples of size 3 from the population. Use either simple random sampling or systematic sampling with the help of the table of random numbers in Appendix A. Calculate the mean for each sample.
Once you have calculated the mean for each sample, calculate the mean of means (i.e., add up your 10 sample means and divide by 10). How does this mean compare with the mean for all states?
How does the value of the standard deviation that you calculated in Exercise 8a compare with the value of the standard error (i.e., the standard deviation of the sampling distribution)?
Construct two histograms, one for the distribution of values in the population and the other for the various sample means taken from Exercise 8b. Describe and explain any differences you observe between the two distributions.
It is important that you have a clear sense of the population that we are working with in this exercise. What is the population?

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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The following table shows the number of active military personnel in 2009, by region (including the District of Columbia).

Pacific	229,634	Mountain	89,816	West South Central	177,336
West North Central	64,564	East North Central	26,384	East South Central	68,440
South Atlantic	376,034	Middle Atlantic	41,441	New England	8,579

How does the value of the standard deviation that you calculated in Exercise 8a compare with the value of the standard error (i.e., the standard deviation of the sampling distribution)?
Construct two histograms, one for the distribution of values in the population and the other for the various sample means taken from Exercise 8b. Describe and explain any differences you observe between the two distributions.
It is important that you have a clear sense of the population that we are working with in this exercise. What is the population?

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