~When performing a hypothesis test, there is a possibility that your conclusion is in error.

~Type I & type II errors focus around the statement in the null hypothesis. The original claim should be addressed in stating them.

~The significance level a (alpha) determines the chance of making a type I  error. That is, the probability of a type I error = a.
What is a type I error?

~A type I error is the error made by rejecting a true null hypothesis (RAT for short).

~Since the significance level a determines the size of the rejection region, we are willing to reject the null hypothesis whenever our sample results in a test statistic that falls within this area.

~For example, if a is .05, we will reject a true null hypothesis 5% of the time. That way, we can keep our error relatively small.  For very important tests, we would probably like to do better. So, a smaller significance level would be used, say .01.

~Beginning students often find it difficult to verbalize Type I & Type II in a given hypothesis test. Let's take some examples.

~Examples of a type I error:

~Say the null hypothesis is that "This new line of cars get 35 mpg in the city" and the consumer groups believe they get less than 35 mpg. The latter would be the alternate hypothesis.

~A type I error is committed, if we reject the null hypothesis when it is actually true. We also must tie in the alternate hypothesis.  By rejecting the null hypothesis, we are accepting the alternate hypothesis. We can verbalize it this way: "concluding that these new line of cars get less than 35 mpg, when, in reality, they get 35 mpg". That way, we are rejecting the null hypothesis when it is really true.

~Let's take another example of a type I error.

~A college representative claims that students average more than 8 hours of sleep/night.. Many others believe that this figure is incorrect. A hypothesis test is set up and done and a type I error is committed. The null hypothesis would be that the students average is 8 hours. The alternate hypothesis is that the students average more than 8 hours. 

~We can verbalize the type I error this way:  "Concluding that the students average more than 8 hours/night, when, in reality, they average 8 hours/night". That way, we are rejecting the null hypothesis, when it is actually true.

~Now, for the type II error.

~The symbol for the probability of a type II error is b. What is a type II error?

~A type II error is made when we accept a false null hypothesis. (AAF for short)

~Let's use the same two examples in this discussion to verbalize the type II error.

~Take the example above of the new line of cars getting 35 mpg in the city. A type II error is committed if we conclude the following: "the new line of cars do get 35 mpg in the city, when, in reality, they really get less than 35 mpg". Notice how I tied in the alternate hypothesis, since there is a direction assumed. That way, we are accepting a false null hypothesis.

~Let's verbalize the Type II error in our second example concerning students at a college averaging 8 hours/night of sleep. We can say it this way: "Concluding that the students average 8 hours/night of sleep, but, in reality, they average more than 8". That way, we are accepting a false null hypothesis.

~Note: Finding the value of beta is no easy task. Go to the following link for details and an example:   Finding Beta