## Hypothesis Testing

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)