ACTIVITY 1.

Objective of this activity to give you an idea on Central Limit Theorem by carrying out some simulations.

In this activity first we will take a sample of size n from a population which has a distribution that is not bell-shaped, such as exponential and uniform. For that sample we will calculate the mean. Then we will take another sample of the same size from the same population and find the mean. We will repeat this simulation m times. Then we will describe the distribution of the sample means (sampling distribution of the sample mean) that we have found by using graphical and numerical methods. Here is what you need to do:

Uniform Population:

• Step 1: Click on the "Generate" button on the Statlets window at the end of this page.
• Step 2: Click on the "Random numbers" button.
• Step 3: Click on the "Uniform" button and type 40 in the "Sample size" box.
• Step 4: Click on the "OK" button.
• Step 5: Type 0 in the left window that appears, this is the c=lower limit, and type 10 in the right window, this is d=the upper limit. Click "OK".
• Step 6: Select the "Histogram" then "Stem-leaf" from menu options. Does the graphs appear to be bell-shaped?
• Step 7: Select the "Stats" from menu options and write the mean on a piece of paper.
• Step 8: Repeat steps 1-7 20 times. You will have a data set consist of 20 sample means.
• Step 9: Select the "Input" from menu options and replace Col_1 with the 20 sample means that you have recorded.
• Step 10: Select the "Histogram" then "Stem-leaf" from menu options. Does the graphs appear to be bell-shaped?

Click on the "Input" menu option. Repeat the above steps for c=-800 and d=1200. Comment on the shape of the histogram and boxplot for these values.

ACTIVITY 2.

Exponential Population

• Step 1: Click on the "Input" menu option.
• Step 2: Click on the "Generate" button on the Statlets window at the end of this page.
• Step 2: Click on the "Random numbers" button.
• Step 3: Click on the "Exponential" button and type 40 in the "Sample size" box.
• Step 4: Click on the "OK" button.
• Step 5: Type 15 in the window that appears, this is the q=mean. Click "OK".
• Step 6: Select the "Histogram" then "Stem-leaf" from menu options. Does the graphs appear to be bell-shaped?
• Step 7: Select the "Stats" from menu options and write the mean on a piece of paper.
• Step 8: Repeat steps 1-7 20 times. You will have a data set consist of 20 sample means.
• Step 9: Select the "Input" from menu options and replace Col_1 with the 20 sample means that you have recorded.
• Step 10: Select the "Histogram" then "Stem-leaf" from menu options. Does the graphs appear to be bell-shaped?