0.6 Central limit theorem: central limit theorem lab i (edited:

Class Time:

Name:

Student learning outcomes:

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

Collect the data

• Using the random number generator in minitab, simulate the tossing of a single die 60 times. Calc ->Random Data ->Integer
• Using Stat ->Tables ->Tally, summarize the data
• Construct a histogram using Minitab and then sketch the graph using a ruler and pencil. Scale the axes.

• Caluclate the following:

  • A

    $\overline{x}$ =

  • B

    $s$ =

  • C

    $n=1$ (single die)
• 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.

• 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.

• Calculate the following:

  • A

    $\overline{x}$ =

  • B

    $s$ =

  • C

    $n=2$ (surveying one person at a time)
• 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.

• Generate fifty groups of 5 die tosses. Record the values of the average of their value.
• 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.

• Calculate the following:

  • A

    $\overline{x}$ =

  • B

    $s$ =

  • C

    $n=5$ (surveying five people at a time)
• 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.

• Generate fifty groups of 20 die tosses. Record the values of the average of their value.
• 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.

• Calculate the following
• 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

• As $n$ changed, why did the shape of the distribution of the data change? Use 1 – 2 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 data? $X$ ~
• In the section titled "Collecting Averages of Groups of Twenty", what was the approximate distribution of the data? $X$ ~
• In 1 – 2 complete sentences, explain any differences in your answers to previous three questions.