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Transcript
7.3 Notes pg. 451-461
(Feel free to add notes of your own.)
AP Exam Tip: Notation matters. The symbols
Μ‚, 𝒙
Μ…, 𝝁, 𝝈, 𝒑, 𝝁𝒑̂, πˆπ’‘Μ‚, 𝝁𝒙̅, πˆπ’™Μ… all have specific and different
𝒑
meanings. Either use notation correctly or don’t 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 𝑛 from a large population with µ and 𝜎.
β€’ Mean of the sampling distribution of π‘₯Μ… is πœ‡π‘₯Μ… = πœ‡
𝜎
β€’ Standard deviation is 𝜎π‘₯Μ… =
𝜎
βˆšπ‘›
β€’ Only use 𝜎π‘₯Μ… =
when the population is at least 10 times as large as the
βˆšπ‘›
sample or 𝑁 β‰₯ 10𝑛
β€’ Sample mean π‘₯Μ… is an unbiased estimator of the population mean πœ‡
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 𝑛 from a population that has the distribution 𝑁(πœ‡, 𝜎).
β€’ Then the sampling distribution of the mean π‘₯Μ… has the distribution 𝑁 (πœ‡,
𝜎
βˆšπ‘›
).
Read Example Young Women’s Heights pg. 455.
Central Limit Theorem
β€’ Draw an SRS of size 𝑛 from any population whatsoever with mean πœ‡ and finite standard
deviation 𝜎.
β€’ When 𝑛 is large, the sampling distribution of the sample mean π‘₯Μ… is close to the
𝜎
normal distribution 𝑁 ( πœ‡, ) .
βˆšπ‘›
β€’ Larger sample sizes are required if shape of the population is far from Normal, in
particular 𝒏 β‰₯ πŸ‘πŸŽ.
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