Hypothesis Testing Applet

This applet illustrates the process and theoretical background of testing the hypothesis of a population mean having a specific value against different alternatives. You should also check out the closely related Central Limit Theorem applet.

Start the HypoTester applet
Carefully move through the four steps involved when testing a hypothesis to understand how the applet works.

Now answer the following questions:

Using the default values, would you feel comfortable rejecting the null hypothesis, and hence accepting the alternative hypothesis ? If so, what is the probability that you are making a mistake when you reject the null hypothesis?
Use the default values, but now choose the "two-sided alternative" in Step 1. Do you still reject the null hypothesis? What is the probability now of making a mistake when rejecting the null hypothesis? What is the relation of this probability to the probability in the previous question? Is that relation always true between one- and two-sided alternatives?
Use the default values, but now choose the "left-sided alternative" in Step 1. How does the result of the test change? Would you still reject the null hypothesis? Why or why not?
Reset all values to their default values by clicking on [Reset]. Now experiment with different standard deviations, keeping all other values the same. How does the result of the test change when you change the standard deviation? Explain.
What does this all have to do with the Central Limit Theorem (you could start the HypoCentral applet to see an illustration of the Central Limit Theorem)