One-Tailed and Two-Tailed Tests (Jump to: Lecture | Video )

Here's an example we've been using for the last few lectures:

School District A states that its high schools have an 85% passage rate on the High School Exit Exam. A new school was recently opened in the district, and it was found that a sample of 150 students had a passage rate of 88%, with a standard deviation of 4%. Does this new school have a different passage rate than the rest of School District A?

The question that's being asked is "Does the school have a passage rate different than 85%?"

This is a two-tailed test, because we are testing to see if the mean is either below or above 85%.

Figure 1.

What if the question was "Does the school have a passage rate greater than 85%?"

This is a one-tailed test, because we are only testing to see if the mean is greater than 85%.

Figure 2.

What if the question was "Does the school have a passage rate less than 85%?"

This is a one-tailed test, because we are only testing to see if the mean is less than 85%.

Figure 3.