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# Hypothesis Testing Simulation

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For this exercise, use n = 100 and the normal distribution with mean 50 and standard deviation 10. Each time you click on Ã¢Ã¢?Â¬Ã…"Simulate,Ã¢Ã¢?Â¬Ã‚? the applet runs 100 hypothesis tests with the conditions you have set and reports the number of times the null hypothesis was rejected, the number of times the null hypothesis was not rejected, and the proportion of times the null hypothesis was rejected at both the .05 and .01 levels of significance.

First, set the null mean equal to 50 and the alternative to Ã¢Ã¢?Â¬Ã…" not equalÃ¢Ã¢?Â¬Ã‚? and run the applet one time by clicking on the simulate button. Answer the following questions:
How many times was the null hypothesis rejected at the 0.05 level of significance?
In this case, the null hypothesis is true. Which type of error occurred each time the null hypothesis was rejected?
What is the probability of rejecting a true null hypothesis at a 0.05 level of significance?
How does the proportion of times the null hypothesis was rejected compare to this probability?
Now clear the applet, then set the null mean equal to 47, and keep the alternative at Ã¢Ã¢?Â¬Ã…"not equal.Ã¢Ã¢?Â¬Ã‚? Run the applet one time by clicking on the simulate button and answer the following questions:
How many times was the null hypothesis not rejected at a 0.05 level of significance?
In this case, the null hypothesis is false. Which type of error occurred each time the null hypothesis was not rejected?
Without clearing, run the applet several more times by clicking on the simulate button. Based on your results what can you conclude about the probability of failing to reject the null hypothesis for the given conditions?