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Central Limit Theorem: Central Limit Theorem Lab I (edited: Teegarden)

Module by: Mary Teegarden. E-mail the author

Based on: Central Limit Theorem: Central Limit Theorem Lab I by Barbara Illowsky, Ph.D., Susan Dean

Summary: Labs changed to incorporate mini-tabs.

Class Time:

Name:

Student Learning Outcomes:

  • The student will examine properties of the Central Limit Theorem.

Collect the Data

  1. Using the random number generator in minitab, simulate the tossing of a single die 60 times. Calc -> Random Data -> Integer
  2. Using Stat -> Tables -> Tally, summarize the data
  3. Construct a histogram using Minitab and then sketch the graph using a ruler and pencil. Scale the axes.
    Figure 1
    Blank graph with frequency on the vertical axis and value on the die on the horizontal axis.
  4. Caluclate the following:
    • a. x¯ x =
    • b. ss =
    • c. n = 1 n=1 (single die)
  5. Draw a smooth curve through the tops of the bars of the histogram. Use 1 – 2 complete sentences to describe the general shape of the curve.

Collecting Averages of Pairs

Repeat steps 1 - 5 (of the section above titled "Collect the Data") with one exception. Instead of recording the value of a single die, record the average of two dice. Use Minitab and generate 50 rows with two columns. Then use the Calc -> Row Statistics and select mean. Then use Stats -> Tables -> Tally to summarize the data.

  1. Construct a histogram. Scale the axes using the same scaling you did for the section titled "Collecting the Data". Sketch the graph using a ruler and a pencil.
    Figure 2
    Blank graph with frequency on the vertical axis and value on the die on the horizontal axis.
  2. Calculate the following:
    • a. x¯ x =
    • b. ss =
    • c. n = 2 n=2 (surveying one person at a time)
  3. Draw a smooth curve through tops of the bars of the histogram. Use 1 – 2 complete sentences to describe the general shape of the curve.

Collecting Averages of Groups of Five

Repeat steps 1 – 5 (of part I) with one exception. Instead of recording the value for a single die, record the average value for each of the 50 groups of 5 die tosses.

  1. Generate fifty groups of 5 die tosses. Record the values of the average of their value.
  2. Construct a histogram. Scale the axes using the same scaling you did for section titled "Collect the Data". Sketch the graph using a ruler and a pencil.
    Figure 3
    Blank graph with frequency on the vertical axis and value on the die on the horizontal axis.
  3. Calculate the following:
    • a. x¯ x =
    • b. ss =
    • c. n = 5 n=5 (surveying five people at a time)
  4. Draw a smooth curve through tops of the bars of the histogram. Use 1 – 2 complete sentences to describe the general shape of the curve.

Collecting Averages of Groups of 20

Repeat steps 1 – 5 (of part I) recording the average value for each of the 50 groups of 20 die tosses.

  1. Generate fifty groups of 20 die tosses. Record the values of the average of their value.
  2. Construct a histogram. Scale the axes using the same scaling you did for section titled "Collect the Data". Sketch the graph using a ruler and a pencil.
    Figure 4
    Blank graph with frequency on the vertical axis and value on the die on the horizontal axis.
  3. Calculate the following
  4. Draw a smooth curve through tops of the bars of the histogram. Use 1 – 2 complete sentences to describe the general shape of the curve.

Discussion Questions

  1. As nn size 12{n} {} changed, why did the shape of the distribution of the data change? Use 1 – 2 complete sentences to explain what happened.
  2. In the section titled "Collect the Data", what was the approximate distribution of the data? XX ~
  3. In the section titled "Collecting Averages of Groups of Five", what was the approximate distribution of the data? XX ~
  4. In the section titled "Collecting Averages of Groups of Twenty", what was the approximate distribution of the data? XX ~
  5. In 1 – 2 complete sentences, explain any differences in your answers to previous three questions.

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