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# Calculation of mean height of children

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I have been given a data set with the heights (in cm) of 200 Mexican children ages 2- 10 years. Each child has an ID number at the column to the left. For the purposes of this assignment, I will think of the 200 children as being a population of children from some town in Mexico. I will need to estimate the average (mean) height of the 200 children based on two random samples.

Your instructions as an EXAMPLE only:

1) With your eyes closed, place your pen somewhere in the random numbers table. Before, you start, you should decide if you will move up, down left, or right through the table.

2) Using the random numbers in order from your start point, select 5 children's ID numbers at random from the table. Calculate the mean height of the selected children based on this sample of size 5 (n=5).
(I have chosen children 115, 116, 117, 118, 119) MEAN= 546.3/5=109.26

3) Repeat the above steps using ten new children (n=10). If you chose the same child twice by chance, pick another child.
(I have chosen children 21, 22, 23, 24, 25, 26, 27, 28, 29, 30) MEAN= 1152.6/10=115.26

4) If you had to guess the average (mean) height of all 200 children, what would be your best guess? Would the mean from the sample of size 5 be a better or more reliable estimate than the mean calculated from the same of size 10? Explain your reasoning.

5) What does the central limit theorem say about repeated sampling? How does the central limit theorem apply to the mean heights calculated from your samples of population of children?

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#### Solution Preview

2. n =5; I will be moving down from a ID at the top and then to the next column.
The mean height of the selected children based on this sample of size 5 (n=5) is 106.8

I.D no. of child Height of the child (cm) Mean/Average Height (cm)
20 117.7 534/5 = 106.8
37 84
50 117.3
79 99.2
189 115.8

3. n = 10; I will be moving similarly down from a ID at the top and then to the next column.
The mean height of the selected children based on this sample of size 10 (n=10) is 118.52

I.D no. of child Height of the child (cm) Mean/Average Height (cm)
4 128.5 1185.2/10 = ...

#### Solution Summary

According to the Central Limit Theorem, the distribution of an average tends to be Normal, even when the distribution from which the average is computed is decidedly non-Normal.

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