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# Week10 - STA 2023 c B.Presnell D.Wackerly Lecture 15...

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STA 2023 c B.Presnell & D.Wackerly - Lecture 15 175 Thought: Too bad that all the people who know how to run the country are busy driving taxicabs and cutting hair! Assignments : Today: P. 265 – 271 For Tuesday: Exercises 6.15, 6.21, 6.24, 6.28, 6.33, 6.37, 6.38, 6.41–46 For Wednesday: P. 280 – 285 For Thursday: Exercises 7.1, 7.3–5, 7.10, 7.11, 7.15–20

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STA 2023 c B.Presnell & D.Wackerly - Lecture 15 176 Recall from last time: If we plan to take a random sample of size from a population with mean and standard deviation , is a random variable. Distribution of is called its sampling distribution. (p. 255) . So is an unbiased estimator of . (p. 266, 261) (p. 266), so dist. of is more concentrated around for larger sample sizes. is called the standard error of .(p. 266) New terms P arameter – meaningful number assoc. with a P opulation . (p. 254) S tatistic – meaningful number assoc. with a S ample . (p. 254)
STA 2023 c B.Presnell & D.Wackerly - Lecture 15 177 Know the mean and standard error of , HOW ABOUT THE DISTRIBUTION ? If the population has a normal distribution, the sampling distribution of is normal, with mean and standard deviation (standard error) . Central Limit Theorem : (p. 267) For large , regardless of the shape of the population dist. the sampling dist. of is : approximately normal with mean standard error . Larger sample size, better approximation. For most populations, is “large enough”.

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STA 2023 c B.Presnell & D.Wackerly - Lecture 15 178 x x original population distribution distribution of when n = 50.
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Week10 - STA 2023 c B.Presnell D.Wackerly Lecture 15...

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