Type I and Type II errors
Choose the value of the mean for the null hypothesis, the form of the alternative hypothesis, the population standard deviation, and the sample size for the hypothesis test. Also choose the value for the true mean of the population - either the same as the hypothesised value, or a different value.
Press CTRL-R to select a new sample of size n from a Normal population, with the given true mean and standard deviation.
The value of the test statistic is shown by the blue line, and the critical region is also shown on the graph.
With the true mean equal to the hypothesised mean, count the number of Type I errors you get from 100 tests. How does this change for different significance levels?
With the true mean different from the hypothesised mean, count the number of Type II errors you get from 100 tests. How does this change the further the true mean is from the hypothesised mean? How does this change for different significance levels?