6.2 Confidence Intervals for the Mean ( unknown) Key Concepts: Properties of the t-distribution Finding Areas Below a t-curve Building and Interpreting Confidence Intervals for the Mean

6.2 Confidence Intervals for the Mean ( unknown) What is the t-distribution? William S. Gosset “Studentized” version of the sample mean If X is normally (or approximately) normally distributed, then the studentized version of the sample mean follows a t-distribution with n-1 degrees of freedom

6.2 Confidence Intervals for the Mean ( unknown) Properties of the t-distribution Bell-shaped and symmetric Shape of the t-curve is determined by the number of degrees of freedom Total area below every t-curve is 1 Mean, Median, and Mode are all zero As the number of degrees of freedom increases, the t-distribution approaches the standard normal distribution

6.2 Confidence Intervals for the Mean ( unknown) Practice working with t-curves #2, 4 p. 315 How do we build these confidence intervals? Note: When we construct “t-intervals”, we use the t-curve with n – 1 degrees of freedom.

6.2 Confidence Intervals for the Mean ( unknown) Practice: #18 p. 315 (Driving Distance to Work) #28 p. 316 (Homework) How do we know whether a z-interval or a t-interval is more appropriate? Flowchart on p. 314 will help More practice: #34 p. 317 (Yards Per Carry) #31 p. 317 (Body Mass Index))