Explain the difference between a left-tailed, two-tailed, and right-tailed test. When would we choose a two-tailed test? How can we tell the direction of the test by looking at a pair of hypothesis? How can we tell which direction (or no direction) to make the hypothesis by looking at the problem statement (research question)? Solution Depending on the alternative hypothesis operator, > will be a right-tailed test, < is a left-tailed test, and is a two-tailed test. Alternative hypothesis has the > operator, right-tailed test Alternative hypothesis has the < operator, left-tailed test Alternative hypothesis has the operator, two-tailed (left and right) test Left Tailed Test H1: parameter < value Notice the inequality points to the left Decision Rule: Reject H0 if t.s. < c.v. Right Tailed Test H1: parameter > value Notice the inequality points to the right Decision Rule: Reject H0 if t.s. > c.v. Two Tailed Test H1: parameter not equal value Another way to write not equal is < or > Notice the inequality points to both sides.