AP Statistics : How to define a Type II error

Study concepts, example questions & explanations for AP Statistics

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Example Questions

Example Question #5 : Inference

If a test has a power of , what is the probability of Type II error?

Possible Answers:

Correct answer:

Explanation:

From the statistical definition of power (of a test), the power is equal to  where  represents the Type II error.

Therefore our equation to solve becomes:

Example Question #6 : Inference

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?

Possible Answers:

Type I and II

Neither

Type II

Type I

Correct answer:

Type II

Explanation:

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 : How To Define A Type Ii Error

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?

Possible Answers:

Type II

Type I and II

Type I

Neither

Correct answer:

Type II

Explanation:

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 #2 : How To Define A Type Ii Error

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?

Possible Answers:

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 the percentage of defective widgets is 1% and the factory claim is upheld.

The test came up with no definitive answer.

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.

Correct answer:

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.

Explanation:

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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