The shape of the Sampling Distributions

Table of Contents

1. Introduction:
2. Overview of the Applet.
3. When the Population is Normal
4. When the Population is Skewed?

Overview of the Applet.

The idea of a sampling distribution is that different samples will produce different statistics. If we take many samples we will see many different statistics. If we take those different statistics and put them into a histogram we can visualize the sampling distribution of the statistic. It is the sampling distribution that allows us to determine many of the elements that we see in research such as margins of error. To help visualize the sampling distribution we can make use of an online simulation what is often called an "applet".

Allow the page to fully load (this may take a moment). When the page has loaded click the button marked "BEGIN".

Assume our population is normally distributed. We would like to take a sample of 5 items from this population. To do this:

1. Set the choice of distribution to "Normal."
2. Next set the statistic to "Mean" and the sample size to N=5.
3. Click "Animated" to see the first sample appear on the section marked Sample Data. A blue mark will appear on the panel marked "Distribution of the Means."

1

Where is the mean of your sample? Look at the left side of the graphic and look at the mean of your sample (it will be indicated in blue to the left of the graph labelled "Sample Data"). a) 0-10 b) 11-29 c) 30-70 d) 71-90 e) 91-100 Correct Check again carefully. Did you follow the directions? Your answer has been saved.

Take a second sample by again clicking on "Animated."

2

Where is the mean of your second sample? Look at the left side of the graphic and look at the mean of your second sample. (notice that both means are represented on the graph marked distribution of means). a) 0-10 b) 11-29 c) 30-70 d) 71-90 e) 91-100 Correct Check again carefully. Your answer has been saved.

Continue to take samples by repeatedly clicking "Animated" until you have taken 10 samples.

3

What is the largest mean? What is the largest sample mean in your sample? Note that you can click on the blue boxes in the graph labelled "Distribution of Means" and the corresponding sample data will reappear. Read the value from the left of the graph labelled "Sample Data". Great. Continue on to the next question.

Rather than repeatedly clicking the Animated button we can click sample numbers of 5, 1000, or 10000. Use the 10000 button to quickly take 10000 additional samples (This may take a second). Observe the shape of the resulting distribution.

4

What shape does the histogram have? Examine the histogram that is given in blue? What shape does this histogram have? a) A normal distribution centered at 10 b) A right skewed distribution. c) A left skewed distribution. d) A normal distribution centered at 50. e) A bimodal distribution. CorrectIncorrect Look carefullyYour answer has been saved.