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7.3 Notes pg. 451-461 (Feel free to add notes of your own.) AP Exam Tip: Notation matters. The symbols Μ, π Μ , π, π, π, ππΜ, ππΜ, ππΜ , ππΜ all have specific and different π meanings. Either use notation correctly or donβt use it at all. You can expect to lose credit if you use incorrect notation. MEAN AND STANDARD DEVIATION OF A SAMPLE MEAN β’ Suppose π₯Μ is the mean of an SRS size π from a large population with µ and π. β’ Mean of the sampling distribution of π₯Μ is ππ₯Μ = π π β’ Standard deviation is ππ₯Μ = π βπ β’ Only use ππ₯Μ = when the population is at least 10 times as large as the βπ sample or π β₯ 10π β’ Sample mean π₯Μ is an unbiased estimator of the population mean π β’ Values of π₯Μ are less spread out for larger samples Example This Wine Stinks pg. 452 Skip the Think About It pg. 453 Sampling Distribution of a Sample Mean from a Normal Population β’ Draw an SRS of size π from a population that has the distribution π(π, π). β’ Then the sampling distribution of the mean π₯Μ has the distribution π (π, π βπ ). Read Example Young Womenβs Heights pg. 455. Central Limit Theorem β’ Draw an SRS of size π from any population whatsoever with mean π and finite standard deviation π. β’ When π is large, the sampling distribution of the sample mean π₯Μ is close to the π normal distribution π ( π, ) . βπ β’ Larger sample sizes are required if shape of the population is far from Normal, in particular π β₯ ππ. Read Example Servicing Air Conditioners pg. 459 Collected HW: pg. 461-463 #54, 58, 66, 68 Due Wed. end of class Suggested problems: #49,57, 59, 65,67