Edit View Insert Format Font Tools Table Window Help Week 4 Graded Problems and

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Edit View Insert Format Font Tools Table Window Help Week 4 Graded Problems and Exercises.docx 1509 SmartArt Review Search in Doc out Elements Tables Charts ?xt Box Shape Pct Pacific West North Central South Atlantic 229,634 Mountain 89,816 West South Central 177,336 64,564 East North Central 26,384 East South Central 68,440 376,034 Middle Atlantic41,441 New England 8,579 a. 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. a. 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? b. c. How does the value of the štandard 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? d. e. Pages:3 of 9 Words: 516 of 1939 SAA Moblle

Explanation / Answer

A. The mean of the population is 120247.6 and the standard deviation is 119819

a.

sample 1 2 3 4 5 6 7 8   

Mean 158143.00 53129.33 151017.67 74273.33 118989.33 30487.00 156952.67 25468.00

sample 9 10

Mean 273502.67 62737.00

b.

The Mean of means = Mean of (158143.00 53129.33 151017.67 ........ 62737.00)

=110470

which is closer to the mean of all states

c.

Standard Error = Standard deviation of (158143.00 53129.33 151017.67 ........ 62737.00)

=76904.64

which is closer to 119819 / sqrt(3) where 119819 is the standard deviation of the population and sqrt stands for square root.

d.

The histogram of sample means is more symmetric(or normal) than the population.

Thank You

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