7.3 Hypothesis Testing for the Mean ( unknown) Key Concepts: Student’s t-distribution Critical Values and Rejection Regions The t-test for a Population Mean

7.3 Hypothesis Testing for the Mean ( unknown) Why do we need another test for µ? If we do not know σ, then we cannot use the z-test from the last section. Instead we use the ‘studentized’ version of the sample mean as our test statistic and the t-distribution to find our critical values. Note: we use n-1 degrees of freedom when we look for our critical values Practice finding critical values: #6 p. 383 (right-tailed test) #8 (two-tailed test)

7.3 Hypothesis Testing for the Mean ( unknown) Things to know about the t-test for µ: Assumes σ is unknown and either the population is normally distributed or n  30. The test statistic is the studentized version of the sample mean: Always use the t-curve with n-1 degrees of freedom.

7.3 Hypothesis Testing for the Mean ( unknown) Guidelines for using the t-Test for µ are given on page 379. #16 p. 384 (IRS Wait Times) #22 p. 384 (Annual Pay)