To set up the test, fill in the boxes: What null hypothesis H0 about the mean μ do you want to test? Which alternative hypothesis Ha do you have in mind, and what level of significance α do you require? What value of the standard deviation σ is known to be true? How many observations n will you have (250 or fewer)?
If you already have a sample mean, enter this value and click UPDATE to display the sample mean on the graph and calculate its statistical significance. Or you can specify the true population mean μ to create a random sample from the population, display the observations and sample mean (note that some of the points in the sample may be too far from μ to appear in the display), and calculate its statistical significance. Click NEW SAMPLE to generate different random samples.
Click the "Quiz Me" button to complete the activity.
This applet illustrates statistical tests with fixed level of significance. Here we're testing a hypothesis about the mean of a normal distribution whose standard deviation we know, but the concepts are essentially the same for any other type of significance test.
The normal curve shows the sampling distribution of the sample mean when your null hypothesis is true and the sample size and population standard deviation have the values you choose. The yellow area under the curve represents the values of that are significant at level α. This area is equal to α, the probability of getting a significant result when the null hypothesis is true.
Suppose you're planning to collect a set of data in an experiment where the null hypothesis states that the population mean will be 15. You will collect 30 observations, and you expect the population standard deviation to be 6.5. You plan to test at the .05 level of significance, using a one-tailed test (that is, testing whether μ < 15). Below, enter the values you would enter in the applet to simulate this situation:
Choose the "I have data, and the observed..." option in the applet, enter this value (13), and click UPDATE.