Hypothesis Testing Tutorial
 A. Introduction Exercise 1: Testing ACE Graduates Related Topics Follow-up

 Pages: A B C D E F G H I J

## C. Sampling Error and Sample Size

The applet below allows us to simulate drawing random samples of VAST test takers from a normally distributed null population with a mean (m) of 500 and a standard deviation (s) of 100.

1. To begin, use the drop down menu under Sample size: and select N=25. Under Show:, check Show sample data and Show population (with no other boxes checked for now).

2. Click Draw a sample to draw a random sample of 25 cases from this population. The individual scores are represented by black boxes and the sample mean is shown with a red arrow.

1=2; 2=5; 3=25; 4=1001=normal; 2 = bin.1; 3 = bin.5; 4 = uni1= means, all else equals cases1 = show sampling dist; otherwise off#include virtual="includes/nojava.ssi"

3. Click Draw a sample at least ten times to observe how a sample mean based on N = 25 is likely to be quite close to the population mean of 500.

4. Click Show obtained means to see your observed sample means.

5. To view the theoretical distribution of all possible sample means based on samples of N = 25 selected randomly from the Null Population, click Show sampling distribution of the mean. The standard deviation of this distribution is the standard error of the mean, shown in the box to be equal to 20.00, the value we computed earlier. Click here to review the computation.

6. To observe the sampling distribution of means for smaller samples with N = 5, use the drop down menu under Sample size: and select N=5. Notice that the distribution of possible means has greater variability. The standard error of the mean is reported in the box to be 44.72. Review computation.

### Question C: Sampling Error

From least to most likely, rank the following events (assume random sampling from the population of VAST-test takers with m = 500 and s = 100):

1. Obtaining an individual score of 550 or greater.
2. Obtaining a sample mean of 550 or greater with a sample size of 25.
3. Obtaining a sample mean of 550 or greater with a sample size of 5.

1, 2 , 3
3, 2, 1
2, 3, 1
Events equally likely.