Practice problems for these concepts can be found at:
 Confidence Intervals and Introduction to Inference Multiple Choice Practice Problems for AP Statistics
 Confidence Intervals and Introduction to Inference Free Response Practice Problems for AP Statistics
 Confidence Intervals and Introduction to Inference Review Problems for AP Statistics
 Confidence Intervals and Introduction to Inference Rapid Review for AP Statistics
When we do a hypothesis test, we never really know if we have made the correct decision or not. We can try to minimize our chances of being wrong, but there are tradeoffs involved. If we are given a hypothesis, it may be true or itmay be false. We can decide to reject the hypothesis or not to reject it. This leads to four possible outcomes:
Two of the cells in the table are errors and two are not. Filling those in, we have
The errors have names that are rather unspectacular: If the (null) hypothesis is true, and we mistakenly reject it, it is a TypeI error. If the hypothesis is false, and we mistakenly fail to reject it, it is a TypeII error. We note that the probability of a TypeI error is equal to α, the significance level (this is because a Pvalue < α causes us to reject H_{0}. If H_{0} is true, and we still decide to reject it, we have made a TypeI error). We call probability of a TypeII error β. Filling in the table with this information, we have:
The cell in the lower righthand corner is important. An honest person does not want to foist a false hypothesis on the public and hopes that a study would lead to a correct decision to reject it. The probability of correctly rejecting a false hypothesis (in favor of the alternative) is called the power of the test. The power of the test equals 1 – β. Finally, then, our decision table looks like this:
example: Sticky Fingers is arrested for shoplifting. The judge, in her instructions to the jury, says that Sticky is innocent until proved guilty. That is, the jury's hypothesis is that Sticky is innocent. Identify TypeI and TypeII errors in this situation and explain the consequence of each.
solution: Our hypothesis is that Sticky is innocent. A TypeI error involves mistakenly rejecting a true hypothesis. In this case, Sticky is innocent, but because we reject innocence, he is found guilty. The risk in a TypeI error is that Sticky goes to jail for a crime he didn't commit.
A TypeII error involves failing to reject a false hypothesis. If the hypothesis is false, then Sticky is guilty, but because we think he's innocent, we acquit him. The risk in TypeII error is that Sticky goes free even though he is guilty.
In life we often have to choose between possible errors. In the example above, the choice was between sending an innocent person to jail (a TypeI error) or setting a criminal free (a TypeII error). Which of these is the most serious error is not a statistical question—it's a social one.
We can decrease the chance of TypeI error by adjusting α. By making α very small, we could virtually ensure that we would never mistakenly reject a true hypothesis. However, this would result in a large TypeII error because we are making it hard to reject the null under any circumstance, even when it is false.

1
 2
Ask a Question
Have questions about this article or topic? AskToday on Education.com
Popular Articles
 Kindergarten Sight Words List
 Signs Your Child Might Have Asperger's Syndrome
 10 Fun Activities for Children with Autism
 Social Cognitive Theory
 Problems With Standardized Testing
 First Grade Sight Words List
 April Fools! The 10 Best Pranks to Play on Your Kids
 Child Development Theories
 Theories of Learning
 The Homework Debate