**Unformatted text preview: ** 156 STA 2023 c B.Presnell & D.Wackerly - Lecture 13 STA 2023 c B.Presnell & D.Wackerly - Lecture 13 157 Thought: Vital papers will demonstrate their vitality by
moving from where you left them to where you can’t ﬁnd Normal Approximation to the Binomial them. Distribution
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¢ 164 STA 2023 c B.Presnell & D.Wackerly - Lecture 13 STA 2023 c B.Presnell & D.Wackerly - Lecture 13 165 Ex. Coin tossing. In 10 tosses, approximate the prob. of
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C § even for 166 STA 2023 c B.Presnell & D.Wackerly - Lecture 14 STA 2023 c B.Presnell & D.Wackerly - Lecture 14 Thought: A truly wise person never plays leap-frog with
a unicorn. . 167 Sampling Distributions Assignments : ¢ Recall (p. 4 – 6), objective of statistics is to make an Today : P. 254 – 264
For Thursday: Exercises 6.1, 6.3, 6.4. 6.8 inference about a population based on information
contained in a sample from the population. ¢ For Monday : SPRING BREAK!!! Desired inference often phrased on terms of one or
more parameters.(p. 254) Last Time : – A Parameter is a meaningful number associated
with a Population.
– Mean ( ), Variance ( A ¥£T §
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£ 172 STA 2023 c B.Presnell & D.Wackerly - Lecture 14 STA 2023 c B.Presnell & D.Wackerly - Lecture 14 173 An unbiased estimator for a population parameter if
(Defn. 6.5, p. 261) the mean of the sampling distribution
of the estimator equals the parameter. is an estimator for $ $
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£¢ ¢ in a sample to compute a single number that we £ a rule or formula telling how to use the use the data $ A point estimator for a parameter (Defn. 6.4, p. 261) . Unbiased
Estimator intend to be “close” to the value of the population
parameter
(popn. µ underestimates Divided by
variance, when we computed the sample to get an unbiased estimator for the 174 Biased
Estimator µ overestimates Tends to overestimate too often.
If we have two unbiased estimators, prefer the one with
the SMALLER standard error. $ ¥ close to ¦ $ $
¥ µ $ µ ¦ close to ) ¢
STA 2023 c B.Presnell & D.Wackerly - Lecture 14 µ µ proportion of the time. population variance , underestimates overestimates Tends to over and underestimate the same ¢ (popn. variance). £P ¦§
¢ ¢ (sample variance) is a point estimator for ) £¢ mean) $ (sample mean) is a point estimator for . ...

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