This applet illustrates statistical tests with fixed level of significance. The setting is the same as Section 6.2 of PBS: testing hypotheses about the mean of a normal distribution whose standard deviation you know.

To set up the test, fill in the boxes: What null hypothesis H_{0} about the mean do you want to test? Which alternative
hypothesis H_{a} do you have in mind? How many observations n will you have (50 or fewer)? What value of the standard deviation
is known to be true? And what level of significance do you require? Then click **Update** to display the information you have entered.

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 chose. The yellow area under the curve covers values of that are significant at level . This area is equal to , the probability of getting a significant result when the null hypothesis is true.

You can enter a sample from data you already have. Use the **Test** button to display this
and its statistical significance. Or you can specify the true population
mean and use the **Generate Sample** button to create a random sample from the population and
display the sample mean from this one sample. Note that some of the points in the sample may be too far from
to appear in the display. Try this both when H_{0} is true and when alternatives are true.