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## 6.2 Confidence Intervals for the Mean ( unknown )

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**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))