SOLUTION: I need help with Type I and Type II error. Explain a factor that the researcher can control to change the Type I error. Explain a factor that the researcher can control to change t

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Question 475048: I need help with Type I and Type II error. Explain a factor that the researcher can control to change the Type I error. Explain a factor that the researcher can control to change the Type II error.
I am not understanding how to respond to this.
Answer by MathLover1(20850) (Show Source):
You can put this solution on YOUR website!
Say you want to test whether a die is biased. You set up an experiment and throw the die 6000 times and count the number of sixes you get.
The null hypothesis is that the die is fine and the probability that a throw shows 6 is 1/6. Generally it needs a bit of thought to find the alternative hypothesis but for the test above it is that the probability is different from 1/6 (that's called a two tailed test because you don't have an opinion about whether you want the true probability to be above or below 1/6)
Next (and we still designing the test here) we decide on the significance level of the test and 5% is fairly normal in these circumstances. In setting it at 5% we are saying that if the result of the experiment is well away fromm 1000 sixes out of the 6000 throws so far away that we know the probability of this happening by chance is less than 5% then we shall report that the die is likely biased. The main maths work in these problems is to find the Critical Region that's the results which will lead you to reject the null hypothesis I'm not showing this work here but for this set up its below 943 and above 1057.
So we do the experiment and say 1070 sixes plenty more than 'expected' and well inside the critical region so we report that the die is biased. But is it? If the die is fair we have made a Type 1 error. There is always a chance that our result however outlandish has occurred simply as part of the random variation.
A type 1 error is when we wrongly reject the null hypothesis. Type 1 errors can not be avoided they are part of the design of the statistical test but they can be made less common by setting the significance (that's the 5% above) at a lower level.
However if we do do set the significance level lower say 1% that increases the chance of a type 2 error.
A type 2 error is when you wrongly fail to reject the null hypothesis. We set the significance level at 1% the Critical region is now over 1074 the result is not in the Critical region and we report that the experiment does not provide evidence that the die is biased - but it is: we made a type 2 error. A good way to reduce the chance of a type 2 error without making more type 1 errors is to increase the size of the experiment throw that die not 6000 times but 60000 times.