Central Limit Theorem (Pocket Change), The Central Limit Theorem | Statistics

Learning objectives

Central Limit Theorem (Pocket Change)

Student Learning Outcome

The student will demonstrate and compare properties of the central limit theorem.

Collect the Data

Count the change in your pocket. (Do not include bills.)

Randomly survey 30 classmates. Record the values of the change in Ch07_lab1_tbl001.

__________	__________	__________	__________	__________
__________	__________	__________	__________	__________
__________	__________	__________	__________	__________
__________	__________	__________	__________	__________
__________	__________	__________	__________	__________
__________	__________	__________	__________	__________

Construct a histogram. Make five to six intervals. Sketch the graph using a ruler and pencil. Scale the axes.

View original figure (external; image not reproduced in this text edition)
Original figure description: Blank graph template. The horizontal axis is labeled Value of the change and the vertical axis is labeled Frequency.
Calculate the following (n = 1, surveying one person at a time):
1. $\bar{x}$ = _______
2. s = _______
Draw a smooth curve through the tops of the bars of the histogram. Use one to two complete sentences to describe the general shape of the curve.

Collecting Averages of Pairs:

Repeat steps one through five of the section Collect the Data with one exception. Instead of recording the change of 30 classmates, record the average change of 30 pairs.

Randomly survey 30 pairs of classmates.

Record the values of the average of their change in Ch07_lab1_tbl002.

__________	__________	__________	__________	__________
__________	__________	__________	__________	__________
__________	__________	__________	__________	__________
__________	__________	__________	__________	__________
__________	__________	__________	__________	__________
__________	__________	__________	__________	__________

Construct a histogram. Scale the axes using the same scaling you used for the section titled Collect the Data. Sketch the graph using a ruler and a pencil.

View original figure (external; image not reproduced in this text edition)

Original figure description: This is a blank graph template. The horizontal axis is labeled Value of the change and the vertical axis is labeled Frequency.
Calculate the following (n = 2, surveying two people at a time):
1. $\bar{x}$ = _______
2. s = _______
Draw a smooth curve through the tops of the bars of the histogram. Use one to two complete sentences to describe the general shape of the curve.

Collecting Averages of Groups of Five:

Repeat steps one through five (of the section titled Collect the Data), with one exception. Instead of recording the change of 30 classmates, record the average change of 30 groups of five.

Randomly survey 30 groups of five classmates.

Record the values of the averages of their change.

__________	__________	__________	__________	__________
__________	__________	__________	__________	__________
__________	__________	__________	__________	__________
__________	__________	__________	__________	__________
__________	__________	__________	__________	__________
__________	__________	__________	__________	__________

Construct a histogram. Scale the axes using the same scaling you used for the section titled Collect the Data. Sketch the graph using a ruler and a pencil.

View original figure (external; image not reproduced in this text edition)

Original figure description: This is a blank graph template. The horizontal axis is labeled Value of the change and the vertical axis is labeled Frequency.
Calculate the following (n = 5, surveying five people at a time):
1. $\bar{x}$ = _______
2. s = _______
Draw a smooth curve through the tops of the bars of the histogram. Use one to two complete sentences to describe the general shape of the curve.

Discussion Questions

Why did the shape of the distribution of the data change, as n changed? Use one to two complete sentences to explain what happened.
In the section titled Collect the Data, what was the approximate distribution of the data?
X ~ _____(_____, _____)
In the section titled Collecting Averages of Groups of Five, what was the approximate distribution of the averages? $\bar{X}$ ~ _____(_____, _____)
In one to two complete sentences, explain any differences in your answers to the previous two questions.

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