AP Statistics : How to define a Type II error
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Example Questions
Example Question #1 : Defining Errors
If a test has a power of 
From the statistical definition of power (of a test), the power is equal to 
Therefore our equation to solve becomes:
Example Question #1 : How To Define A Type Ii Error
You and a classmate wanted to test the effect of sugars and fats on levels of blood sugar.
Your classmate told you that they found the null hypothesis valid, which was what there is no difference between the effects of sugars and fats on blood sugar levels.
If the null hypothesis was actually false, what type of error was made?
Type I and II
Type I
Neither
Type II
Type II
A type I error occurs when the null hypothesis is valid but rejected.
A type II error occurs when the null hypothesis is false, but fails to be rejected.
Because the null hypothesis was false, but had failed to be rejected, they made a Type II error.
Example Question #1 : Defining Errors
You and a friend wanted to test the effect of similar servings of juice and soda on blood sugar levels.
Your friend told you that they found the null hypothesis valid, which was what there is no difference between the effects of similar servings of juice and soda on blood sugar levels.
If the null hypothesis was actually false, what type of error was made?
Type I
Type II
Type I and II
Neither
Type II
A type I error occurs when the null hypothesis is valid but rejected.
A type II error occurs when the null hypothesis is false, but fails to be rejected.
Because the null hypothesis was false, but had failed to be rejected, they made a Type II error.
Example Question #1 : Defining Errors
A factory claims that only 1% of their widgets are defective but a large amount of their produced widgets have been breaking for customers. A test is conducted to figure out if the factory claim of 1% defective is true or if the customers claim of graeater than 1% is true. What would be an example of a Type II error?
The test came up with no definitive answer.
The test shows that the percentage of defective widgets is 1% and the factory claim is upheld.
The test shows that only 1% are defective when the truth is that more than 1% are defective. The null is upheld when it should be rejected.
The test shows that there are more than 1% defective even though the null of just 1% is actually true.
More than 1% are shown to be defective and the reject the factory claim of only 1% defective.
The test shows that only 1% are defective when the truth is that more than 1% are defective. The null is upheld when it should be rejected.
Type II Error is not rejecting a truly false null hypothesis. This means that the test supports the factory claim of 1% even though the true amount is more than that.
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