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?

When the Population is Normal

What impact does the shape of the parent population have on the shape of the sampling distribution of the mean? We can experiment with this by using the applet with various settings.

Sample size n=5.

Begin by opening the applet:

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

How many items in the sample? Look at the second graphic labelled "Sample Data". After you hit the "Animated" button some boxes appeared on this second graphic. How many of these boxes appeared? a) 2 b) 4 c) 5 d) 16 e) 25 Correct there are 5 observations in our sample. Incorrect. Is your sample size set to 5? Your answer has been saved.

4. Click the 1000 button 5 times to produce over 5000 sample means.

2

Shape of the histogram of the means? Examine the histogram of the sample means (the blue histogram). What shape does this histogram have? a) Skewed to the right b) Skewed to the left c) Symmetric but not at all like a normal distribution. d) Similar to a normal distribution. Correct. The sample means had a normal distribution.Incorrect. Look carefully at the blue histogram. Your answer has been saved.

Sample size n=25

1. Set the choice of distribution to "Normal."
2. Next set the statistic to "Mean" and the sample size to N=25.
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."

3

How many items in the sample? Look at the second graphic. After you hit the "Animated" button some boxes appeared on this second graphic. How many of these boxes appeared? a) 2 b) 4 c) 5 d) 16 e) 25 Correct there are 25 observations in our sample. Incorrect. Is your sample size set to 25? Your answer has been saved.

4. Click the 1000 button 5 times to produce over 5000 sample means.

4

Shape of the histogram of the means? Examine the histogram of the sample means (the blue histogram). What shape does this histogram have? a) Skewed to the right b) Skewed to the left c) Symmetric but not at all like a normal distribution. d) Similar to a normal distribution. Correct. The sample means had a normal distribution.Incorrect. Look carefully at the blue histogram. Your answer has been saved.

Sample size n=100

1. Set the choice of distribution to "Normal."
2. Next set the statistic to "Mean" and the sample size to N=100.
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."
4. Click the 1000 button 5 times to produce over 5000 sample means.

5

Shape of the histogram of the means? Examine the histogram of the sample means (the blue histogram). What shape does this histogram have? a) Skewed to the right b) Skewed to the left c) Symmetric but not at all like a normal distribution. d) Similar to a normal distribution. Correct. The sample means had a normal distribution.Incorrect. Look carefully at the blue histogram. Your answer has been saved.

Summarize the results

6

Which were like a normal distribution? Review the experiments you did with the different sample sizes. In which of the sample sizes did the sample means (blue histogram) resemble a normal distribution? (Pick all that apply). a) n=5 b) n=25 c) n=100 Correct. For any sample size (even a sample of just 5 observations) the sample means resemble a normal distribution.Is that all of them? Look back over your experiments and try again.Your answer has been saved.